107-119
MODELING EIGENVECTORS WITH GIVEN THE VALUES OF THEIR INDICATED COMPONENTS
Authors: Sapargali Zhanatauov
Number of views: 281
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 ckj=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), where 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.