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www.T-Science.org       p-ISSN 2308-4944 (print)       e-ISSN 2409-0085 (online)
SOI: 1.1/TAS         DOI: 10.15863/TAS

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## ISJ Theoretical & Applied Science 03(71) 2019

* Scientific Article * Impact Factor 6.630

Zhanatauov, S. U.

### A matrix of values the coefficients of combinational proportionality.

Scientific Object Identifier: http://s-o-i.org/1.1/TAS-03-71-31

Language: Russian

Citation: Zhanatauov, S. U. (2019). A matrix of values the coefficients of combinational proportionality. ISJ Theoretical & Applied Science, 03 (71), 401-419. Soi: http://s-o-i.org/1.1/TAS-03-71-31 Doi: https://dx.doi.org/10.15863/TAS.2019.03.71.31

Pages: 401-419

Published: 30.03.2019

Abstract: The article solved a new spectral problem - ISP 6, inverse to the Direct Spectral Problem [3]. For known values of the eigenvalues ?1,…,?n, ?nn=diag(?1,…,?n) such that ?1>…>?n>0 and the known and given values of some components of the n eigenvectors с1,…,сn from the matrix Cnn=[с1|…|сn]of eigenvectors to find:1) new model values of known, but not given, values of the components of n pseudoeigen vectors с+?+1,…,с+n, с+j=(с+1j,с+2j…с+nj)Т, j=1,…,n,, from the new matrix +nn=[с+1|…|с+n] pseudoeigen vectors; 2) the resulting matrix of eigenvalues ? +nn should have the values equal to 1: ? +nn=diag(1,…,,1) = Inn. 3) the resulting full matrix of eigenvalues ?+nn=Inn and the matrix of pseudoeigen vectors C+nn=[с+1|…|с+n] must satisfy the equalities C+ТnnC+nn?Inn,C+nnC+Тnn=Inn, C+nn?+nnC+Тnn=Inn, сj+?+nnсj+T=1,сi+?+66сj+T=r+ij=0,r+ij=r+ji=0, i=1,…,n;j=1,…,n,i?j, and the correlation matrix R+nn=C+nn?+66C+Тnn=Inn should have new matrices of pseudoeigen vectors C +nn ? Inn and eigenvalues ?+nn=Inn=diag (1,…,1),?+1=…=?+n=1, ?1+…+?+n=n. In ISP 6 introduced new terms "coefficient of combinational proportionality" (CCP), " pseudoeigen vectors". In the developed models ISP 4, ISP ISP5, ISP 6, Optimization Problems were formulated and solved with the corresponding assumptions on their parameters and variables. Model C+nn-samples Z(t)mn=U(t)mn[C+nn]T,t=1,…,kt, (reproduced not by the known spectrum of the correlation matrix) were used to solve the problems of “extracting digital knowledge "of digital data from different subject areas, means of cognitive modeling. An example of modeling and visualization of a “figure from m points” inside an n-dimensional bal is given. It illustrates model uncorrelated z-variables corresponding to their cognitively independent meanings.

Key words: coefficient of combinational proportionality, pseudoeigen vectors, C+-sample, ? –sample.

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