Meanings as guiding our lives Returning to the moments of childhood already described, we can complete the actual picture of the formation of meanings in a child as guiding life. I will begin by describing an example from the life of one of my acquaintances. I won't stop myself from

Recently, many people began to notice that something is happening on our planet and it is time for change. Only you can decide how you want to live your life. And once you decide, you must take responsibility for that decision. We are controlled by instilling a sense of fear in us through the media. And yet, many people are beginning to wake up, become aware, and begin to live differently.

Many actions of people are not the result of their own conscious conclusions and desires, for the most part, people obey the laws of the Matrix. Since childhood, people have been in her networks, we are literally “Children of the Matrix”. The main principle of the Matrix is ​​that people do different things, that are part of the game and act according to a pre-programmed principle. The essence of the principle is that the chain of actions and deeds supposedly necessary for a person should increase in mathematical progression.

VIRTUAL NIGHTMARE x/f (the idea is deeper than in the Matrix.)

The biggest incentive and driver in this chain is money. A person wants to constantly spend and accumulate them, and the stronger the desire of a person to have as much money as possible, the stronger the principles of the Matrix act on him. Money is the so-called knowing, Babylonian magic. After all, only money can buy all the benefits of civilization. However, a person does not understand that his life does not depend on the amount of money. This is one of the most important and basic tricks of the Matrix and, of course, a means of managing people. It is difficult for a person to understand that, having been drawn into the magic of money, they begin to control him.

A person gets into the Matrix from the very conception, and a person simply has no other choice, he does not know anything other than the Matrix. Its principle works flawlessly, since a person, having once acted as he had to act from birth, becomes part of the Matrix. A person becomes a slave of the Matrix for life. They are controlled in many ways. Money and the media are the main drivers of escapism. Specially designed technical innovations are also such stimulants and controls, people are hooked when they are constantly waiting for the invention of a new technical innovation. The very subtle part of the Matrix is ​​built on the principle of invisible control through invisible "operators" of consciousness that control our instincts and emotions. The Matrix uses levers of pressure on us, through the qualities that are inherent in every person - these are Ego, Morality and Emotions.

One of the main principles of the Matrix is human overload with an endless stream of information.

Much of the information people perceive serves as an anchor that does not allow a person to catch the essence.

To prevent the possibility of the emergence of their own elite groups in the mass of the ruled, it needs to be completely silenced. Thus, in the modern West, a phenomenon has arisen that has been called “democracy of noise”. Such a sound (and noise) design of the surrounding space has been created that the average person practically does not have sufficient intervals of silence to concentrate and think through to the end a coherent thought. This is an important condition for his defenselessness against the manipulation of consciousness. The elite, on the other hand, values ​​silence very highly and has the economic opportunity to organize their lives outside the "democracy of noise."

A person cannot even realize whether it is good or bad for him to live in this Matrix, since he does not know what freedom from the Matrix is ​​and how one can live differently.

It is impossible for someone who was born in captivity and lived in it all his life to realize and feel the taste of true freedom.

Who rules the Matrix? This is a philosophical question. It is more important to understand that the Matrix is ​​a prison for growing souls incarnated on the Planet, but The overseers are part of it too. They fulfill the architect's plan!

The most important task of the Matrix is ​​to manage people, society must be a large, faceless, controlled mass.

People were created their own little world and they figured out what they should do in this little world of theirs so that they would have an incentive to live and lack of time and opportunity to figure everything out.

Invented values ​​and activities invented by someone take up almost all of a person’s time, and as a result, it is much more important for a person to put on a suit and go to work than to stop and understand why he is doing it. And this process, once launched, cannot be stopped until a person clearly realizes that he is in the Matrix and lives with his eyes closed, one might say, sleeps.

The difference between the Matrix and reality lies in the complete freedom of choice and in the awareness of this freedom. The world outside the Matrix is ​​completely different, the way you would like it to be. You just have to take a step and get out of the Matrix to see it with your own eyes.

How to do it?

Everything is simple, and at the same time difficult. Gotta stop thinking common clichés and stereotypes, work on yourself and your old worldview, use your mind and intuition to the fullest, do not stop in search of the truth, but go on and on looking for it, listen to your heart.

There will be like-minded people from those people who have already left the Matrix. So far there are very few of them, but they are and are here on our planet in order to help us take a step and get out of this enveloping web, whose name is the Matrix.

You must wake up, realize that you are in prison, break out of its networks and embark on a path that leads to freedom, real life and true happiness.

Overcome your Fear, you need to realize that you yourself create your life with your actions and thoughts. Learn to stop the hustle and bustle of life and be alone with yourself for a while. Learn to listen to the real you from the inside.

Our life on Earth is only a small part of our Path, our goal is much more...

Soul incarnations

The Matrices of Life are the objective conditions for the emergence and realization of our desires. The character of each person and his environment are formed, depending on how much energy is in each of his matrices. Life goals and obstacles on the path also depend on which matrix dominates in each of us. In any matrix, we find both positive and negative qualities: both pleasant and useful, and harmful and unpleasant. None of the Matrices of Life can be ignored: lack of energy will immediately affect our well-being, relationships, and standard of living.

How matrices program our lives

I want to remind you that the lack of awareness in our lives leads to the fact that we are more easily succumbed to external influences and are more willing to dance to someone else's tune. And first of all it concerns our matrices. For each of us, all four matrices are worked out differently and, therefore, we are not alike and live differently. But there are many coincidences in life when different people behave in a similar way.

Simple explanation: all people are essentially the same. Correct explanation: different people may have the same degree of elaboration of certain matrices.

At the same time, in the same situations, different people can behave differently. Simple explanation: everyone is different. Correct explanation: even people who look similar to each other may differ in the degree of elaboration of certain matrices.

An important point, especially for those who like to rely on other people in difficult situations. The behavioral responses of people in stressful and emergency situations can be completely unexpected and not consistent with the prevailing impression of them. That is, when you need help, you may not get it from the person you hope for. And in this, in fact, he will not be to blame.

I am stating this not in the context of public morality and the principle of forgiveness. My point of view is formed by understanding the influence of the energies of the Matrices of Life on all levels of our being. Our thinking, our habits, our desires and way of life are subject to the laws of matrices. And we can notice and realize this in order to help ourselves work through each of the matrices as quickly as possible.

But often, even knowing the features of the manifestation of the energy of the matrices, we can succumb to some kind of temptation, for example, alcohol, break loose on a loved one or show indecision at an important moment. And this happens under the influence of the energy of the matrices. These matrices program our behavior and our life.

We can try to resist this programming. But, in this case, the question arises: maybe this resistance is also programmed by matrices? If we do not put everything on the shelves, then we will get confused in these reflections.
First, what is a program.

A program is a specific sequence of actions set in order to achieve a specific result.

And we follow the programs that are defined for us by our matrices. It should be noted that we can talk about our programs in two directions. Directions are defined by such concepts as a good matrix and a bad matrix.

A good matrix is ​​a well-developed matrix that allows you to use your energy in a timely and efficient manner in the right situation. It saves you from unnecessary problems in life. A good matrix programs our actions in a positive way. We can say about a person “he has a good such-and-such matrix”, if we notice that his actions, his behavior are in harmony with external conditions.

For example, a driver humbly waits for the green signal of a traffic light and his car does not take off, as in Formula 1 races, but starts off smoothly and drives in its direction. And we can state that this driver has a good second matrix. And he patiently and consistently follows the rules of the road.

A bad matrix is ​​an undeveloped matrix, which brings many difficulties into our lives due to incorrect or untimely application of its energy in a particular situation. In this case, the whole life can be spoiled by a continuous stream of problems. A bad matrix programs our actions in a negative way. We can say about a person “he has such a bad matrix” if we notice that his actions, his behavior are not harmonious.

There are many examples of a bad matrix in everyday life. These are beggars with their bad first matrix, and pedestrians crossing the street at red lights with their bad second matrix, and losers at school who do not see the point in studying and have no goal of achieving academic success with their bad third matrix.

The main program for us is to work through all the matrices and reach a new level of life, a new level of consciousness. And we can go through a full cycle by working through our matrices. A new level will not be available to us if we cannot cope with the previous level.

The transition to the next matrix means that the stage of dominance of the energy of the previous matrix is ​​over, and the stage of mastering the next matrix begins.

The most important thing to know about matrices is that no one can avoid going through all the matrices.

And, even if someone manages to skip one of them on one cycle of life, then on the next one he will still have to return to the matrix and go through it, but this will be twice as difficult. Because a bad matrix will only get worse.
If we talk about programs within each individual matrix, then good matrices program our behavior so that our situations develop according to the hierarchy of matrices, so that the energy level rises. In this case, more and more pleasure and more and more success become available to us.

Our bad matrices, on the contrary, program us for destructive behavior, when we harm ourselves and others. There is a positive aspect to this - by our inharmonious manifestations, we can guess that we are not all right with the energy of the matrices. But more often than not, we get ourselves in trouble by trying to fulfill our desires without having enough energy to do so.

The most correct way to change the negative programs of the matrices is to study the matrices. We may feel or notice that our behavior is not harmonious, that we are harming ourselves. But by working through the matrices, we prevent the negative consequences of bad matrix programs.

For example, impatience creates many problems. But, remaining conscious, noticing your impatience, you can keep yourself from reckless actions. Although this will be very difficult with an undeveloped second matrix, it is still possible. And a little bit of agonizing waiting each day is enough to train your second matrix. Some negative programs will quickly disappear.

You can take examples of negative programs from life without leaving your home, just watching the news on TV.

Here are some of them:
- the desire for self-destruction through addiction to drugs;
- "beautiful" life through theft, robbery and violence;
- sinking to the bottom of society due to unwillingness to work;
- mental deviations due to the loss of meaning in life;
- excessive physical and emotional stress for career growth;
- victory at any cost, when athletes use doping that destroys the body;
- refusal to follow the rules of the road, which creates chaos on the roads;
- the inability to earn enough money, which leads a person to a debt hole;
- excessive patience, leading to severe chronic diseases;
- addiction to adrenaline, leading people to life-threatening situations and death;
- the inability to make independent decisions, which leads to complete dependence on someone else's power and someone else's opinion
and much more.

Of course, our task is to erase negative programs. This cannot be done on a mass scale, each person must decide for himself whether to work out his matrices or not. I believe that each of us has a choice, regardless of the dominant matrix. After all, in any case, the other matrices are also represented in the potential of each of the people. I will try to do everything so that after reading the book each reader has his own individual method of working out his matrices.

How is it that we attract certain situations

In each case of diagnosing a specific situation, we will get our own picture. And this picture will already contain not only a diagnosis, but also a prescription. You just need to have a good understanding of the matrix features, the features of each matrix, and what should be done with it in order to change the situation for the better.

And here it should be remembered that the best is not what we want, but what will allow us to follow the Laws of the Matrices of Life. Or even so: the best desire is the one that does not contradict the Laws of the Matrices of Life. Yes, laws are sometimes harsh, but they regulate and direct life in the right direction. After all, we all want success! And we all have the potential to achieve this success.

While we have undeveloped matrices, we need to be prepared for the fact that we also have the potential to fail. Each of us has ever faced the fact that we found ourselves in an unexpected or unpleasant situation for ourselves. And some people in their lives do nothing but attract trouble.

From mouth to mouth, stories are passed about those people who seem to be lucky in everything. They seem to attract good luck, wealth and the right people. At the same time, a person himself can practically do nothing specifically for this. They say about such people that they have good karma, or in our case, a good matrix.

Karma in Hinduism defines the relationship between cause and effect. In Russian culture, this is reflected in the expression that you reap what you sow. And we will refer to the laws that are called karmic because they determine what consequences our certain actions will have.

Karmic Laws are the hidden mechanism of the Universe, which determines the sequence of passing the steps of Life.

Each step is described by the Matrices of Life and is obligatory for every living being to pass. If a person has not mastered some matrix during his lifetime, he will again and again return to the same situation in order to work it out. This confirms the theory of multiple lives.

The multiplicity of lives and the predestination of events is an ancient theme. And we will not ignore it because we are interested in one interesting question: why is one person born active in life and lucky in business, while the other looks like a squishy guy from childhood and has been unlucky all his life in everything.

Here, of course, the energies of the Matrices of Life are involved. The combination of the energies of the matrices creates a special field of attraction for the corresponding situations in which people find themselves. By understanding the principle of this attraction, we can predict what situation a person will attract in the next moment of his life.

For example, an excessively slow person gets into situations that shake him up, trying to revive, start and accelerate his movement to a higher level. A person who is too hasty often finds himself in situations that are aimed at tempering his ardor a little, slowing down a little. And he, as it were, attracts obstacles to himself, forgetting to draw up some necessary document, without making an important call, etc.
A girl who took part in our seminars told the story of her friend's life. A friend is a classic representative of the second matrix with a predominance of negative manifestations. Everything in her life is difficult for her. She works hard, but does not get a promotion, she went to live abroad, hoping to get rich, but in two years she could not get a residence permit.

Accidentally finding herself in the border zone while traveling, she fell under the article and was almost expelled from the country. While returning, she got into a car accident - another car crashed into her car, which was not insured. When she came to visit one of her friends, she was bitten by a small, gentle dog, who had never bitten anyone before. However, this girl does not change anything in life. And her bad stories continue.

It happens that inveterate lazy people find themselves at the slot machine at the moment when the jackpot falls out there. They find wallets with money (and of course they do not look for the owner), they are given expensive gifts, although they themselves have never given anything to anyone. It used to be a mystery to me.

Now this riddle has been solved with the help of the Matrices of Life. After all, it is their energy that determines what situations the person who possesses them will attract. And most often, those people who have the energy of the first matrix in sufficient quantities are lucky in life. But do not rush to envy them, they have their own difficulties. You will find the details of their lives in the chapter on the Matrix of Bliss and Peace.

The combinations of matrix energies in each person are not random. They are compiled by the person himself, even if he did nothing for this. That is, inaction in situations where you need to make active efforts also shape our future events. It is not for nothing that the Criminal Code specifies responsibility, including for inaction when nothing prevents one from acting.

But in the case of the energies of the matrices, we may be hindered by their insufficient concentration. Well, where can I get patience, sorry if my second matrix is ​​barely breathing. The energy of the third matrix can help here in order to set a goal to achieve a specific result - to learn patience and endurance. This will allow me to control my behavior, and even if it will be very difficult for me, I will be able to endure, survive it without losing heart.

Knowledge about the Matrices of Life opens up new opportunities for us to improve our lives. We can now pay attention to those features of our behavior that previously seemed normal and harmless to us. Now I can access a resource that was of no interest to me before because I didn't know how to use it. And now I can tell you how to compensate for the lack of energy of one matrix with the energy of another matrix. We will talk about this a little later.

It is important to remember that we are shaping our future, in which we will have to deal with what is happening now. After all, nothing in life is free, everything has its meaning. And, if now we do not notice that our actions, our thoughts somehow influence us, then in the future it may become too obvious for us.

Accordingly, our present is also a reflection of what we have done in the past. And this applies not only to the life that we remember as our own. After all, being born in a family of complete alcoholics or drug addicts, a child pays for something with his torment, but what did he manage to do in this life? From the perspective of working out the matrices, it becomes clear to us that this is not a punishment, but a chance for their more successful processing. In addition, we are waiting for the study of the features of each matrix. And then we will find out what we can fix right now to make our life happy, desires fulfilled, and the wallet full. After all, each of us has the opportunity to correct our situation with the energies of the Matrices of Life, so that the cycle of incarnation, the study of the matrices, is consciously completed. And we could be sure that in the next life we ​​would not step on the same rake.

Even if I have not convinced you that we are not living for the first and not the last time, you will still feel calmer in your soul because the energy in the matrices circulates along a full trajectory and does not cause you unnecessary problems. Achieving this will require FROM us a little attention to our matrices. And what and how to do you will learn from my practical recommendations in the process of presenting our topic.
But let's continue in order.

Life scenarios based on the nature of the energies of the matrices

For example, with the help of matrices, one can explain why a person cannot achieve success in some business, why he is sick, or why he has no chance of achieving anything in life at all. But you can also suggest the path that will lead a person out of this situation, something that will help change events for the better and give a chance to his life.

Usually people do not add up everything that happens in their life into a big picture. But you and I have a good opportunity to look at the life of other people from the outside with the help of the Life Matrix model. This clearly shows how well-developed matrices create a positive picture of life, and undeveloped matrices create a negative one.

Here are a couple of real life scenarios based on the same prevailing matrix.

Scenario one, negative

For a while, the woman enjoyed the sweet life, not burdening herself with the development of intellect, and did not burden herself with thoughts about her future. Her present suited her completely. After a couple of years, the man was fed up with her company and, having sold his business, left the city, leaving the woman some money. She was fired from the salon, because she was of no value as an employee and now she was no longer the wife of the owner.

The woman was left alone with two children, but, as before, she was not going to burden herself with work for the sake of a salary. Money was constantly lacking, so she began to deny herself cosmetics, clothes and medicines. As luck would have it, she accidentally fell on her left hand and it swelled from a severe bruise. This woman was not going to go to hospitals and spend money on medicines, so soon her hand began to lose sensitivity and was partially paralyzed. But the woman was assigned a disability pension, and this saved her from starvation.

She constantly repeated that she needed money, and that soon all her debts would be returned to her. Although all her friends knew that she did not lend money to anyone. Over time, the poor fellow sank lower and lower, her health deteriorated, her teeth blackened from coffee and cigarettes, and she became like a homeless person. She was no longer recognized by her old friends, because she was used to getting everything for free, for free, so to speak. And the only breadwinners were the daughters, who by that time had grown up.

It is known that this woman has already become like an old witch without teeth and all in wrinkles, although she is no older than her former friends. And they are only forty. She hardly leaves the house, she got herself some kind of mongrel, she probably picked it up on the street and there is a very unpleasant smell in her apartment.

This whole story would seem to me a fiction if I did not know that this is the real story of a living person. And now I know how normal people turn into downtrodden dirty vagrants and homeless people. This is a classic example of the negative effects of being stuck in the first matrix. When consciousness functions at the consumer, almost animal level.

Scenario two, positive

When the girl grew up, she went to college and studied diligently. She wasn't a crammer, but she remembered just enough to get her grade. Gradually, she earned a reputation as a good student and she was automatically given tests. Even at the institute, the girl began to save a little money, without spending money on cosmetics and perfumes.

They did not give her gifts, but sometimes she allowed herself something fashionable from clothes. She had few clothes, but she wore them for a long time and carefully. Which allowed her to save regularly from what her parents gave her to live on. After graduation, she was recommended to a good company in her specialty. A few years later, the young woman was promoted in position and salary. She already had enough money in her account to take out a loan for an apartment.
She met a young man, but was in no hurry to get married. Young met for several years on the same days in the same place. During this time, the girl paid off the loan, and became the head of the department. She and her fiancé got married and bought a car. Then they built a cottage and had a child.

Over time, the family changed their apartment to a more spacious one. And we decided to have another child. In the summer they constantly disappear in the country, diligently grow all sorts of vegetables and make preparations for the winter. I heard that the couple decided to update their car. External crises do not interfere with their measured life, because they can not only endure adversity, but also managed to save up something for a rainy day. Many of their acquaintances envy their constancy, not understanding how it is possible to live like this, without passions and violent emotions, intrigues and risky plans.

And this is an example of a classic good second matrix, on the basis of which such life scenarios unfold. They reflect the ideal of the inhabitant, which all wise rulers dream of seeing in their country.

The term "matrix" has many meanings. For example, in mathematics, a matrix is ​​a system of elements that looks like a rectangular table; in programming, a matrix is ​​a two-dimensional array; in electronics, a set of conductors that can be closed at their intersection points. Poker chips are also directly related to the matrix. Poker chips are made of high quality composite material, often with a metal core. In turn, the composite material or composite has a matrix and reinforcing elements included in it (the exception is layered composites).
The matrix in photography is an integrated circuit (analog or digital-analog), which consists of photodiodes (light-sensitive elements). Thanks to the photosensitive matrix, the optical image projected onto it is converted into an analog-type electrical signal, and if there is an ADC in the matrix, the conversion occurs into a digital data stream.
The matrix is ​​the main element of digital cameras, all modern video and television cameras, cameras built into mobile phones and video surveillance systems.

The main meaning of the term "matrix" is in mathematics.

A matrix is ​​a mathematical object written as a rectangular table of ring or field elements (for example, integer or complex numbers), which is a collection of rows and columns at the intersection of which its elements are located. The number of rows and columns of the matrix determines the size of the matrix. Although triangular matrices, for example, have historically been considered, nowadays one speaks exclusively of rectangular matrices, since they are the most convenient and general.

For the first time, matrices were mentioned in ancient China, then called the “magic square”. The main application of matrices was the solution of linear equations. Also, magic squares were known a little later among Arab mathematicians, around that time the principle of matrix addition appeared. After developing the theory of determinants in the late 17th century, Gabriel Cramer began developing his theory in the 18th century and published Cramer's rule in 1751. Approximately in the same period of time, the “Gauss method” appeared. Matrix theory began its existence in the middle of the 19th century in the works of William Hamilton and Arthur Cayley. Fundamental results in matrix theory are due to Weierstrass, Jordan, Frobenius. The term "matrix" was coined by James Sylvester in 1850.

Matrices are widely used in mathematics for the compact representation of systems of linear algebraic or differential equations. In this case, the number of matrix rows corresponds to the number of equations, and the number of columns corresponds to the number of unknowns. As a result, the solution of systems of linear equations is reduced to operations on matrices.

Matrices allow the following algebraic operations:

• addition of matrices having the same size;
• multiplying matrices of an appropriate size (a matrix with n columns can be right multiplied by a matrix with n rows);
• multiplication of a matrix by an element of the main ring or field (i.e. scalar).

Matrix is ​​a set of numbers that form a rectangular table that contains m - rows and n - columns. The inscription is used to designate the matrix:

and ij , where i is the row number, j is the column number

Matrices C and D have sizes of 3x3 and 2x2. When the number of rows of a matrix is ​​equal to the number of its columns, the matrix is ​​said to be square. So the matrix C is a square matrix of the third order, and the matrix D is a square matrix of the second order.

A matrix that contains only one row or one column is called a vector. In such matrices, one can distinguish a row vector and a column vector. Thus, matrix K is a row vector, and matrix F is a column vector.

A square matrix in which the main diagonal contains non-zero elements, and all the rest are zeros is called a diagonal matrix. The matrix L is a diagonal matrix of the third order. If non-zero elements are only equal to ones, then this is an identity matrix, it is always denoted by the letter E. In our case, the matrix E is also a third-order identity matrix.

If all elements of a matrix are zero, then it is a zero matrix. For example, the matrix V is a zero matrix of the third order.

If we swap rows and columns in a given matrix, we get a transposed matrix of the given one. For example, given a matrix M, each row of this matrix will be transferred to the corresponding column of the matrix next to it in the figure. The second matrix is ​​the transposed matrix of matrix M.

By the middle of the XIX century. matrices have become independent objects of mathematical research. By this time, the rules for addition and multiplication of matrices had been formulated. The main role in their development was played by the work of Hamilton, Cayley and Sylvester (J.J. Sylvester, 1814-1897). The modern designation for the matrix was proposed by Cayley in 1841. The studies of Weierstrass (K.Th.W.Weierstrass, 1815-1897) and Frobenius (F.G.L. Frobenius, 1849-1917) advanced the theory of matrices far, enriching it with new content.

But there is also a special kind of matrix called a magic square. magic square - a square table of integers in which the sums of the numbers along any row, any column, and any of the two main diagonals are equal to the same number.

The magic square is of ancient Chinese origin. According to legend, during the reign of Emperor Yu (c. 2200 BC), a sacred tortoise surfaced from the waters of the Yellow River, on the shell of which mysterious hieroglyphs were inscribed and these signs are known as loshu and are equivalent to a magic square. In the 11th century they learned about magic squares in India, and then in Japan, where in the 16th century. Magic squares have been the subject of an extensive literature. He introduced Europeans to magic squares in the 15th century. Byzantine writer E. Moskhopoulos. The first square invented by a European is A. Durer's square depicted on his famous engraving Melancholy 1. The date of the engraving (1514) is indicated by numbers in the two central cells of the bottom line. Various mystical properties were attributed to magic squares. In the 16th century Cornelius Heinrich Agrippa built squares of the 3rd, 4th, 5th, 6th, 7th, 8th and 9th orders, which were associated with the astrology of the 7 planets. There was a belief that a magic square engraved on silver protected from the plague. Even today, among the attributes of European soothsayers, one can see magic squares.

In the 19th and 20th centuries interest in magic squares flared up with renewed vigor. They began to be investigated using the methods of higher algebra and operational calculus.

Magic squares of odd order can be constructed using the method of a 17th-century French geometer. A. de la Lubera. Consider this method on the example of a square of the 5th order. The number 1 is placed in the central cell of the top row. All natural numbers are arranged in a natural order cyclically from bottom to top in the cells of the diagonals from right to left. Having reached the upper edge of the square (as in the case of the number 1), we continue to fill in the diagonal starting from the bottom cell of the next column. Having reached the right edge of the square (number 3), we continue to fill in the diagonal coming from the left cell with the line above. Having reached a filled cell (number 5) or a corner (number 15), the trajectory descends one cell down, after which the filling process continues.

Where else are matrices used?

The multiplication table is the product of the matrices (1,2,3,4,5,6,7,8,9)T × (1,2,3,4,5,6,7,8,9).

In physics and other applied sciences, matrices are a means of recording data and transforming them. In programming, in writing programs. They are also called arrays. Widely used in technology. For example, any picture on the screen is a two-dimensional matrix, the elements of which are the colors of the dots.

In psychology, the understanding of the term is similar to this term in mathematics, but instead of mathematical objects, some "psychological objects" are meant - for example, tests.

In addition, matrices are widely used in economics, biology, chemistry, and even marketing.

The authors also found an abstract model - the theory of marriages in a primitive society, where, using matrices, allowed marriage options for representatives and even descendants of a particular tribe were shown, which was evidence of the diverse use of matrices.

Now let's take a closer look at some areas of application of matrices.

Consider the theory of marriage, which has already been mentioned.

In some primitive societies, there are strict rules about when marriages are allowed. These rules are aimed at preventing marriages between too close relatives.

These rules allow precise mathematical formulation in terms of "p-matrices". One of the first to state these rules in the form of axioms was Andre Weil.

The rules of marriage are characterized by the following axioms:

• Axiom 1: Each member of society is assigned a certain marriage type.
• Axiom 2: Two individuals are allowed to marry if and only if they belong to the same marriage type.
• Axiom 3: The type of an individual is determined by the sex of the individual and the type of his parents.
• Axiom 4: Two boys (or two girls) whose parents are of different types are themselves of different types.
• Axiom 5: The rules allowing or not allowing a man to marry his relative depend only on the type of relationship. In particular, a man is not allowed to marry his sister.
• Axiom 6: For any two individuals, one can specify such descendants of them who are allowed to marry.

It follows from the axioms that it is necessary to specify a relationship between the type of parents and the types of sons and daughters.

To establish the relationship of kinship, the following designations were used:

Here are some examples of relationship types:

The concept of a matrix and the branch of mathematics based on it - matrix algebra - are extremely important for economists. This is explained by the fact that a significant part of the mathematical models of economic objects and processes is written in a fairly simple, and most importantly, compact matrix form.

Using matrices, it is convenient to write down some economic dependencies.

For example, consider the table of distribution of resources for individual sectors of the economy (conventional units):

This table can be written in a compact form as a resource distribution matrix by industry:

In this entry, for example, the matrix element = 5.3 shows how much electricity is used by industry, and the element = 2.1 shows how much labor is consumed by agriculture.

Raven's progressive matrices - a test for visual and at the same time abstract thinking on analogy(intelligence test), developed by English. psychologist J. Raven (1938).

Each task consists of 2 parts: the main drawing (some kind of geometric pattern) with a space in the lower right corner and a set of 6 or 8 fragments located under the main drawing. From these fragments, it is required to choose one that, being put in place of the gap, would exactly fit the drawing as a whole. Raven's progressive matrices are divided into 5 series of 12 matrices each. Due to the increase in the number of matrix elements and the complication of the principles of relationships, the tasks gradually become more complicated both within the same series and when moving from series to series. There is also a light version of Raven's progressive matrices, intended for the study of children and adults with mental disorders.

The figure shows examples of such matrices:

We have considered the main areas of application of matrices. It turned out that this term is used not only in mathematics, but also in other sciences, such as computer science, biology, chemistry, physics, psychology, economics, etc. In addition, matrices can be practically applicable, for example, as they did in a primitive society to determine the permitted options for marriage.

MATRIX- (German, Matrize, from Latin matrix uterus). 1) in the foundry industry: a copper mold for casting letters, as well as coins. 2) in typography: a paper mold for casting a stereotype.

With the help of matrices, you can solve systems of equations, it is convenient to represent any data in them.

Thus, we came to the conclusion that matrices were widely used and are still used.

Literature:

1. Krass M.S., Chuprynov B.P.; Mathematics, Peter, 2005.
2. Solodovnikov A.S., Babaitsev V.A., Brailov A.V., Shandra I.G.; Finance and Statistics, 2000.
3. Kremer N.Sh.; UNITY-DANA, Higher Mathematics for Economists, 3rd edition, 2007.
4. Wenger A.L. - Psychological drawing tests: An illustrated guide.
5. Encyclopedic Dictionary of a Young Mathematician. - M .: Pedagogy, 1989.