So is the image of the matrix? Formation of a matrix of a complete image with an environmentally friendly elements of a complex object

Have vector space V over a decent field P tasks line operator .

Value 9.8. Core a linear operator  to be called without vectors in the open space V, of rank є is a zero vector. Accept meaning for the community: Ker, tobto.

Ker = {x | (NS) = o}.

Theorem 9.7. The core of the linear operator є wide open space V.

Business value 9.9. Size the kernel of the linear operator is called defect line operator. dim Ker = d.

Business date 9.10.The way line operator  be called a lineless image vector in the open V... Signed for the community Im, tobto. Im = {(NS) | NS V}.

Theorem 9.8. Image line operator є open space V.

Business value 9.11. Size the image of a linear operator is called rank line operator. dim Im = r.

Theorem 9.9. Space Vє the direct sum of the kernel and the image of the given linear operator. Sum to the rank and defect of the line operator V.

Application 9.3. 1) In the open space R[x] ( 3) know the rank of the defect operator differentiation. It is known that there are no transportation costs. Zero stage grinding chain, even, Ker = {f | f = c) that d= 1. Lonely baggage, steps of which I don’t cross three, I’m setting up without fail, feet of which I don’t cross two, now, Im =R[x] ( 2) ta r = 3.

2) Yaksho line matrix task operator M(), then for the meaning of the core you need virishity рівняння  ( NS) = O, like in the matrix form of the viglead, as follows: M()[x] = [O]. Z the basis of the kernel of the linear operator є the fundamental set of solutions of the one-line system and linear equations from the basic matrix M(). The system will be converted to the image of a line operator put vectors  ( e 1), (e 2), …, (e n). The basis of a chain of systems of vectors is a basis for the image of a linear operator.

9.6. Return line operators

Viznachennya9.12. Linear operator  be called werewolf yakscho isnu line operator ψ such scho to visit parity ψ = ψ = , de is the same operator.

Theorem 9.10. Yaksho line operator  beastly, then operator ψ to be called by one rank and called thugs for operator .

Wow operator, beep for operator , stand for  –1.

Theorem 9.11. Line operator  turnover tody and only tody, if the reverse matrix M(), if M( –1) = (M()) –1 .

From the theory of pumping, which is the rank of the reverse line operator of the road rozmіrnostі space, and the defect is expensive.

Butt 9.4 1) Visnichiti, chi beastly lyniyny operator , which is  ( x) = (2NS 1 – NS 2 , –4NS 1 + 2NS 2).

Decision... Warehouse matrix of the whole line operator: M() =. So yak
= 0 then the matrix M() non-gate, and that means, non-gate and linear operator .

2) Know line operator, zombie to the operator , yaksho (x) = (2NS 1 + NS 2 , 3NS 1 + 2NS 2).

Decision. The matrix of the whole line operator, rivna M() =
, werewolf, scraps | M()| ≠ 0. (M()) –1 =
to that  –1 = (2NS 1 – NS 2 , –3NS 1 + 2NS 2).

Value 1. The image of the line operator A is called the impossibility of all the elements represented in the view.

The image of a linear operator A is a linear open space. Yogo size is called operator rank A.

Value 2. The core of the linear operator A is called the impossibility of all vectors that are.

The core is in line with the vastness of the space H. Yogo size is called operator defect A.

If the operator A is in the world space X, then it is fair to start the relationship + =.

Operator A be called non-virtual that's the core. The rank of a non-virgin operator is suitable for space X.

Nekhai - the matrix of the linear transformation of A to the space X in the deyakom basis, to coordinate the image and the prototype related to the relationship

To that the coordinates of any vector are satisfied with the system

It looks like a vivid, but the kernel of the linear operator is a linear envelope of the fundamental system and the solution of the whole system.

Zavdannya

1. Bring the rank of the operator to the same rank of the matrix in the correct basis.

Count the kernels of the linear operators given to the singular basis in the space X by the forward matrices:

5. To bring, scho.

Calculate the rank and defect of the operators given by the starting matrices:

6. . 7. . 8. .

3. VLASNI VECTORS THAT VLASNI VALUES OF THE LINE OPERATOR

The line operator A is easily visible, and the world is open to the space of H.

Viznachennya. The number l is called in the vasnimals of the operator A, like, like, scho. At the same time, the vector is called the power vector of the operator A.

Those who have chosen the power of the power vectors of the line operator and those who have power vectors, are shown in pairs to different powerful values Linear Square

Якшо is the matrix of the linear operator A in the basis of space X, the power value l and the power vector of the operator A start with the next rank:

1. Vlasnі meaning is to know as the root of the characteristic level (algebraic level):

2. Coordinates of all linear independent vectors, which show the skin okremovy value, to gain the system of one-sided linear alignments:

matrix which maє rank. Fundamental solution of the system є vector - one hundred percent of the coordinates of the power vectors.

The root of the characteristic value is also called the power values ​​of the matrix, and the solution of the system is called the power vectors of the matrix.

butt. Know the power of the vector and the power of the operator A, given in the basis of the matrix

1. For the value of the authorities, the value of the warehouse is characteristic for the value of the warehouse:

Zvidsy vlasne value, yogo multiplicity.

2. For the designation of the power vectors in the warehouse and the virtual system of rivnyans:

Equivalent system of basic equivalents of ma viglyad

To that, the skin-hair vector є is a vector-hundred-point, de z is a constant.

3.1. Simple structure operator.

Viznachennya. Linear operator A, which in the n - world space is called an operator of a simple structure, as well as displaying n linearly independent vectors. In general, it is possible to create a basis for the vastness of the power vectors of the operator, in which the matrix of the operator is the simplest diagonal view

de - vlasnі value of the operator. It’s smart, well, and it’s better: if the basis of space X has a matrix of the operator, then the basis is folded from the power vectors of the operator.

Linear operator A є by the operator of simple structure and mode, if the dermal value of the multiplicity is shown in a line-by-line way of independent vectors. So, as the vlasn_ vector is the solution of the system, the same, the cutaneous root of the characteristic equal multiplicity is responsible for the assignment of the matrix to the rank.

Whether it is a matrix of size, which is shown to the operator of a simple structure, suitable to a diagonal matrix

de the matrix of the transition T from the outward basis to the basis of its vectors, by its own hundred vectors of the coordinates of its vectors in the matrix (operator A).

butt. Bring the matrix of the line operator to the diagonal view

In a way, it is characteristic of the same root.

The stars are of the magnitude of the multiplicity and multiplicity.

Perche is not meaningful. Youmu display power vectors, coordinates of є

system solutions

The rank of the given system and the road is 3, that є deprives one of the independent decisions, for example a vector.

Vlasny vectors, which are displayed, are based on the rivnyan system

the rank of which is 1 і, also, there are three linear independent solutions, for example,

In such a rank, the cutaneous value of the multiplicity is shown equally linearly independent vectors and, also, the operator є is the operator of a simple structure. Transition matrix T ma viglyad

and connections between matrices and matrices

Zavdannya

Know the power of the vector and the power of the meaning

line operators, given by the deyakom basis by matrices:

On the other hand, the beginning of the line operators can be brought to a diagonal transition to a new basis. Know the whole basis of the given matrix:

10. To bring the line operator's vector to the different sizes line-to-line.

11. Bring, if a linear operator A, that is, dіє, there are n different values, then whether a linear permutation operator from A, is a basis of power vectors, moreover, whether a power vector A will be available і for B.

ІНВАРІАНТНІ ПІДПРОСТРИ

Value 1.. The space L of the linear space X is called invariant from the operator A, but also to X, as for the skin vector its image can also be found.

The main powers of the invariable spaces in visas are as follows:

1. If both are invariant spaces for operator A, then the sum is also invariant for operator A.

2. If space X is folded into a direct sum of spaces and () and invariably A, then the matrix of the operator in the basis, which is the same basis and the block matrix

de - Square matrices, 0 - null matrix.

3. The skin invariant operator A has one power vector.

stock 1. The kernel of a deyak operator A, ranked X, is discernible. Come on. Todi, fragments of a zero vector will take place in the skin lineal space. Otzhe, the core is invariably A pidprostir.

stock 2. Let the operator A set the matrix for the basis of space X and start with equal

5. To bring, be it a kind of space, an invariable one, a non-virgin operator A, if an invariable one vocal operator.

6. Come on line-up A -worldly space in the basis of a diagonal matrix small items on diagonal. Know all the space, the invariable, and that is the number.

1

Establishing the principles of integrating discrete information when distribution Elements of a folding object є an urgent interdisciplinary problem. At the statti, the process of prompting the image of the object is looked at, which is a complex of blocks, leather on one set of other elements. As a result, there was a conflict in the situation, and some of the won’s stably passed the field of respect for the consistent strategy of information analysis. Furnish the situation bully warehouse parts ob'єkta і okremo were taken as a prototype of the conflict. The zeal of this robot was in the mathematically rotated matrix, as it represented the image of the problem situation. The revision of the design was based on the data of the visual analysis of the design of the graphic composition, the elements of which were given to the situation. The size and graphic features of the elements, which can be vibrated, and also the roses in the composition served as an indicator for seeing the rows and hundreds of images in the matrix. Previously, it has shown that the design of the matrix is ​​based on, in the first place, the behavioral motivation, in other words, the causal inheritance of the situations of the situation and the last time the information of the third You can take into account that the matrix vector principle is meant to form the image of the behavioral situation characteristic for the inducement of the images and those objects on which the respect is directed.

visualization

take off

discreteness of information

1. Anokhin P.K. Narisi in Physiology functional systems... - M .: Medicine, 1985 .-- 444 p.

2. Ilyin V. A., Poznyak E. G. Linin algebra: textbook for universities. - 6th kind. - M .: Fizmatlit, 2004.280 p.

3. Lavrov V.V. Mozok that psycho. - SPb .: RGPU, 1996 .-- 156 p.

4. Lavrov V.V., Lavrova N.M. Infused aggression on the efficiency, integrity, value and sub-activity in the image of a conflict situation // Cognitive psychology: interdisciplinary awareness and practice. - SPb .: VVM, 2015 .-- S. 342-347.

5. Lavrov V.V., Rudinskiy A.V. The triad of strategies for processing information in case of recognition of incomplete healthy images // Fundamental dosage. - 2014 - No. 6 (2). - S. 375-380.

6. Lavrov N.M., Lavrov V.V., Lavrov N.V. Media: comparing various solutions. - M: OPPL, 2013 .-- 224 p.

7. Shelepin Yu.U., Chikhman V.M., Foreman N. Analysis of the dosage of photographing fragmentary images - the whole process of receiving and photographing for informative signs // Russian Physics Journal. 2008. - T. 94.No. 7. - S. 758-776.

The results of the finalization of incomplete images broadened the perspective of the development of principles, so that the integration of discrete information and the installation of complex images began. An analysis of the peculiarities of the recognition of fragmentary images in the presence of a number of fragments, which can change, allowing the use of three strategies to induce a common image in the minds of the lack of information. The strategies were based on the assessment of the significance of the ready-made information portals for the formation of a cliched image. In addition, the skin strategy was characterized by the manipulation of the car parameters of the available information portals. The first strategy conveyed the equivalence of the fragments in the image - the yogh description of the accumulated information up to the level, sufficient for the new detection of the object, should be presented. Another strategy was organized on a differentiated approach to the assessment of the fragments of the current information. The assessment was given based on the hypothesis, how to hang up, but the day of the object. The third strategy began with the motivation of the maximum victoriousness of the gothic information, as it was hoped for a high vagoyu that vvazhalsya acquaintance with the prototype of the real object. An important moment in the history of the robot is the view of the brain mechanisms, which have forgotten the change of strategy, in view of the dominant emotions and behavioral motivations. Lose on respect for nonspecific systems and the brain and the heterogeneity of neuronal modules, which is controlled by the central control. Carrying out of the preliminaries, like that, as well as from the literary dzherel, have lost sight of the nutritional principles of information distribution in a general way. For the purpose of feeding the bully, it is necessary to be careful to form the image of that object, which for a trivial hour has a respect and lack of an innocent image of the strategy to induce the image. Yak such an object could serve the conflict situation, some of it stably passed the field of respect for an unimportant other strategy for the analysis of the situation. The two sides saw the first strategy through the increased triviality of the conflict and adopted the third strategy, uniquely gracious decisions.

Tsil These robots fooled the principles of the matrix in order to induce the matrix to the image on the basis of the elements of information, on the basis of the elements of the information, on the basis of the components integrated ob'єktu, on the yak the bulo is straight uvagu. They saw the following: in the first place, they vibrated the object, at which stable trivial hour of the bullet was taken, on the other hand, they used the method of visualizing the image; formulate the principle of the integral growth of fragments in the matrix.

Materials and methods of presentation

Yak a bagatocomponent object, which has stably changed over to the field of respect with an unconditional strategy of analysis of the useful information, served as a problematic behavior situation. The problem of a violent conflict among family members, as well as intellectuals and educational institutions. Experiments, in which the analysis was carried out according to the method of the situation, overwhelmed the media, which was straightened on the regulation of rubbing between the two sides. Before the ear of meditative negotiations, the representatives of the spirited parties rejected the proposition of the brothers, the fate of yak viprobuvani in experiments with victorious methods of analyzing the situation. The visualization technique transformed into a graphic composition, as it imparted a design to an image, which would be used to identify the components of a complex object with some sprinkling. The technique served as a tool for the further development of the processes of forming a complete image of a set of elements, related details of the object. The group of pre-adolescents consisted of 19 women and 8 people from 28 to 65 years. To reject a civilized visual image of the situation, before the last years, the following events were missed: 2) assess the furnishings for the significance of the day-to-day situation; 3) distribute furnishings on friendly and unwelcoming for the transmission of a conflict and try to simulate the connections; 4) look for a graphic element (colo, square, tricycle, line or point) for skin conditions, to characterize the situation; 5) formulate the composition of graphical elements, the importance of the interconnection of the surroundings, which is transmitted by the multiple elements, then paint the composition on the paper arch. The graphic compositions were given to the analysis - the order was assessed in the order and the relation of the size of the elements to the image. Some kind of out-of-order compositions appeared, but viprobauanim became aware of the interconnection between the situations of the situation. The results of a well-thought-out analysis of the composition of the boule are organized for the formulation of the mathematical rotation of the matrix to the image.

Results of further discussion and discussion

Skin graphic composition, with vip tests, presenting the construction to the image of a behavioral situation, an original one. Apply the compositions and paint the little one.

Graphic compositions, showing the images of problematic behavioral situations, in some of them they had viprobuvans (a skin element of the composition reflects the situation)

The non-repetition of the compositions testified about the previous development before the analysis of the situations with the changes in the rice. The number of elements in the composition and the size of the elements, as well as the design of the composition, provided an assessment of the complex of furnishings.

In addition, as the originality of the compositions was determined, it was developed until the appearance of important features of the design of the image. Pranguchi to induce the whole composition, so that they depict the image of the situation, in the process of probing the elements were subdivided into their own individual likeness, as well as to fix the causal inheritance of the times of the past Seven years old were willing to montuvati the composition at the viglyadi baby, which prompted what kind of visibility began in advance by folding a figurative plan. In fig. 1 (a, b, d) nadajutsya butt of such compositions. Two before the last, before the folding of the composition, formed an idea, laid down by the basis of the plan, apparently, but five times intuitively, did not give a logical explanation, which was why the selected version was taken into account. Some twenty before the last set up a schematic composition, brutal respect for the deprivation of the causal-inherited ring of the furnishings and one hour at a time (Fig. 1, c, e, f). Tied and knitted after an hour of furnishing, they were worn by the composition. In the experiments, there was no interpretation of the day-to-day confrontation with the results of graphic compositions. Such an interpretation was taken over the course of the media, if the parties were ready to negotiate.

The analysis of the compositions, allowing the quest to be perceived, and the universality of the principles to form the image of the situation. In the first place, the compositions were composed of graphical elements, leather from which visualizing the furnishings, which were not very high-quality. The range of the furnishings of the ball is zoomed in by causal and time-consuming changes. In a different way, furnish mali with a non-similar significance of the day-to-day problematic situation. To do the furnishings we looked at the car parameters. Highly significant furnishings were represented by graphical elements in the smallest size, somewhat less significant. The special features were assigned to the image when the matrix was folded to the image. To rely on respect, how large and graphic features of elements, how to vibrate, and also the vastness of the position in graphic compositions served as an indicator for prompting the information matrix, how the situation presented the image mathematical model... A straight-cut matrix, served at the view of tables, divided into rows that are 100%. Rows were seen in the matrix of a completely formed image of a problematic situation, in which there were important elements of prototypes, united by causal and inherited and time-consuming signals, and a hundred, in which parameters are taken into account in the data

(1)

The skin is surrounded by a row of visualizing the form of the part to the image abo, apparently, the prototype of the object. In more rows and more in m, in total, the object was totally removed, some of the more structural and functional authorities, which served as prototypes. The number of hundred nths starts with a number of details, which are meant for every hour to inspire the prototype. You can take into account that more information fragments have been accumulated in the high and low vagi, then a more prototype of the reality. Matrix (1) was characterized by dynamism, some of the world was changing, as far as the image of the captured object was concerned.

Here it is pre-vernacular that the rotation is not the only indicator of the quality of the image. The images presented on the canvases of the artists are most often used to create photographs from the details of the reality, but at the same time you can reverse the association with the other images, to awaken the provocation of emotions. The value of the amn parameters, which means a lot of information fragments, is not very much appreciated. The improvement of the vagueness did not improve the lack of production. Yak showed the advanced strategies of non-meaningfulness, the recognition of the high significance of the Gothic fragments of information, accelerated the adoption of solutions to the problematic situation.

Also, the process of forming a whole image is provided for the interpretation, as well as for bringing it into the information management framework of the matrix. Manipulation turns around in a pretty or mimicry (by means of a straightforward or intuitive unrecognized) change in car parameters in information fragments, to a change in the value of amn. At the same time, the value of bm will change, as it characterizes the significance of the prototype and the resulting image br will change overnight. As soon as it turns to a matrix model, the image is formed, but it is eager for the supremacy of the given object, the organization of the image is described by the offensive rank. Let us mean the vector of inverse images, where we can put m components through

de T is the sign of the transpose, and the skin element of the vector of the prototype of the ma viglyad:

To vibrate the resulting image, you can follow the Laplace rule:

de br is the final result of the formation of a whole image, where, with its components, the value bm, amn is a complex value, which starts the position of the parameters that change in the row, which appears to the prototype. In the minds of the interconnected information, the result can be adjusted for the additional adjustment of the value of the readings.

At the completion of the discussion of the material presented, the principles of formulating the image are followed by respect for the need to concretize the term “image”, which is reflected in the literature from the outside world. The term in front of it means the formation of a whole system of information fragments, which show the details of the object, which is in the field of respect. Moreover, great details of the object are captured by the informational fragments, so that they become prototypes. Yak ob'єkt can be an object, a phenomenon, a process, and a behavioral situation. Formation of the image to be taken care of by the associations of the acquired information and the same, as to take revenge in the memory and is tied with an object, so that it can be taken off. Consolidation of information fragments and associations in the case of the formation of the image is implemented within the framework of the matrix, the design and vector of which are vibrated in an intuitive manner. Vibir lie in the middle of the road, scho to ask the motivations of behavior. Here, especially, respect for the main point - the discreteness of information, as vikoristovuyutsya for the installation of a whole matrix of the image. The integrity, as shown, is taken care of by nonspecific systems in the brain, which controls the processes of analysis of the information and integration in memory. The range can be determined at the lowest values ​​of n and m, equal to one. The image of the increased value with the additional improvement of the vehicle parameters in the available information, and the increase in the image of the growth with the increase in the value of n and m (1).

Visnovok

The visualization of the elements in the image allowed the simplicity of the ambush of the construction in the minds of the surrounding environment of the problematic behavioral situation. As a result of the robotics, it was shown that, in a general way, it is possible to see how the information fragments in the matrix structures can be discerned. The design of this vector begins, in the first place, by the behavioral motivation, in another way, by the causally inherited kind of surroundings that time-consuming information is rejected, as well as, in the third form, the visual fragments of The integrity of the matrix in order to ensure that the integration of discrete information is not taken into account, so that the image can be viewed. Nonspecific systems and the brain store a mechanism that is related to the integration of information in an integral manner. The formation of matrix principles in the form of a folding object expands the perspective of the intelligent nature as a whole, and of the power of the image. To rely on respect for the integrity and preservation of the figurative system, as well as the value of that sub'activity, is encumbered by the non-stagnant new information about the object.

Library

V.V. Lavrov, O.V. Rudinskiy FORMATION OF THE MATRIX OF THE CILE IMAGE AT THE ROSE SPRINKING ELEMENTS IN THE INTEGRATED OBJECT // International Journal of Applied I fundamental doslіdzhen... - 2016. - No. 7-1. - S. 91-95;
URL: https://applied-research.ru/ru/article/view?id=9764 (date of the blast: 01/15/2020). Proponently to your respect magazines, which are seen at the Academy of Natural Sciences

Change of coordinates of the vector and matrix of the operator during the transition to a new basis

Don't bother a linear operator for space in yourself and don't bother in a linear space for vibrano two bases:

Matrix standing here m in the center of the є coordinate of the hundredth basis vector in the "old" basis is called the matrix of the transition from the "old" basis to the "new"“. If now the coordinates of the vector are in the "old" basis, and the coordinates of the same vector are in the "new" basis, then there is no difference

Oskіlki raskladannya on the basis of dine, then vidsy vipliv, scho

The offensive result is trimmed.

Theorem 1.Coordinates of a vector in the basis of the coordinates of the same vector in the basis of interconnected relations (2), de the matrix of the transition from the "old" basis to the "new" one.

Surprising now, as the matrices are tied between themselves and the same operator in different bases and spaces of the Matrix, and they begin by realities.

and in the basis of matrix equivalence (here we take the same meaning, scho i (1)). Vikoristov's theorem (1), matimemo

oskіlki stovpets are happy, then we will recognize the equality

An offensive result has been achieved.

Theorem 2.As the matrix of the operator in the basis, and the matrix of the same operator in the basis then

Respect 1. Two powerful matrices and linked matrices of deyak non-virgin matrix are called sub-matrices. In such a rank, there are two matrices of the same operator in different bases of the same operator.

stock 1. The matrix of the operator in the basis of the ma viglyad

Know the matrix of the th operator at the basis Calculate the coordinates of the vector at the basis

Decision. The matrix of the transition from the old basis to the new one that is ringing to it

Therefore, by Theorem 2, the matrix of the operator is a new basis as follows:

Note 2. It is possible to publish the result to the operator, from one line to another. Let the operator go from the linear space to the line spaceі do not have two bases in the space of vibrano: і and in space - two bases і Todі can be combined with two matrices and a linear operator

and two matrices and the transition from "old" bases to "new" ones:

It doesn’t matter to show, but it’s worth it.

Let the line operator be given to go from the line to the line. The onset of the understanding is crimson at the first line of the line.

Value 1. Kernel operator call yourself helpless

Operator image call yourself helpless

It doesn't matter to bring the same hardness.

Theorem 3.The core is the image of the line operator in the line of open spaces and for the most part, and at the same time

To calculate the kernel of the operator, it is necessary to write down the equivalents in matrix forms (vibrating bases in the open spaces and apparently) and to develop a general algebra system. Explainably now, it is possible to calculate the range of the operator.

Let the matrix of an operator in bases і Meaningful through a hundred of matrices of matrices The belonging of a vector to an image means that there are numbers such that the vector can be represented in a view. є an element of space line combinations Vibrated in a wide range of bases (for example, the maximum number of linear independent columns of the matrix), the image is calculated matrix operator: and then let's see the image of the operator:

Guidedly, the butt of the nucleus is calculated in the form of an operator, which is free from space in itself. And here the basis and start.

stock 2. To know the matrix, the kernel, and the image of the operator projecting onto the area (the trivial space of geometric vectors).

Decision. Viberemo in a spacious basis (for example, a standard basis). In general, the basis is the matrix of the operator of the design to go from the equality of the known images of the basis vectors. So yak flat pass through all that

In such a rank,

Otzhe, the matrix of the operator

The kernel of the matrix operator is computable from the equation

In such a rank,

(good post).

The image of the matrix operator of tension on all lines Independent 100% matrices, tobto.

(most of the time).