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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 11(67) 2018 * Scientific Article * Impact Factor 6.630

Zhanatauov, S. U.

### Modeling eigenvectors with given the values of their indicated components. Scientific Object Identifier: http://s-o-i.org/1.1/TAS-11-67-18

Language: Russian

Citation: Zhanatauov, S. U. (2018). Modeling eigenvectors with given the values of their indicated components. ISJ Theoretical & Applied Science, 11 (67), 107-119. Soi: http://s-o-i.org/1.1/TAS-11-67-18 Doi: https://dx.doi.org/10.15863/TAS.2018.11.67.18

Pages: 107-119

Published: 30.11.2018

Abstract: The paper solves a new problem inverse to the problem from the DSP model: Rnn=>(Cnn, nn) and different from the problem from the model ISP 1: nn=>(C( )nn,R( )nn), =1,…,k < . For the matrix Cnn =[C+1 C2] (with the new values c+kj, j=1,...,l,k {1,...,n}) is required to find a new pair of matrices (C+nn, +nn), such that the matrix C+nn=[C+1C+2] has the same set of pairs of indices (k,j) and the same new values of the components с+kj, j=1,...,l,k {1,...,n} as in the first l eigenvectors с+j=(с+1j,с+2j…с+nj)Т, located at column submatrices С+1 of matrix С+nn=[с+1|с+2|…|с+n]. Matrix С+nn and +nn satisfy the equations: C+ТnnC+nn=C+nnC+Тnn=Inn,C+nn +nnC+Тnn=R+nn, +1+…+ +n=n,сj+ +nnсj+T=1,сi+ +nnсj+T=r+ij, r+ij=r+ji, i=1,…,n;,j=1,…,n, C+nn=[С+1 С+2], where the correlation matrix R+nn has a new matrix of the eigenvektors and the eigenvalues +nn=diag( +1,…, +n)=n. +1+…+ +n=n, +1 … +n >0. Model ISP 2: Cnn=>(C+nn, +nn). The solution of the problem:a pair of matrices +nn,C+nn=[C+1C+2] necessary to implement IM PCA: (C+nn,, +nn)=>(R+nn,Z(t)mn,Y(t)mn), t=1,…,kt< .

Key words: eigenvectors with given the values of their indicated components.

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