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[8]: 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[3]: (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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