The interval estimate on the singular values of Sylvester-Kac matrix
Using n+1 order permutation matrix,the Sylvester-Kac matrix is transformed into a four blocks matrix with two zero blocks on the main diagonal and two non-zero blocks on the diagonal.Then,by utilizing the equivalent relationship between the eigenvalue decomposition problem of matrix A and the singular value decomposition problem of matrice AA*,as well as the Gerschgorin disk theorem of matrices,Hermite matrices,and properties of positive semidefinite matrices,interval estimates of m singular values of tridiagonal matrices are obtained.We also obtained an interval estimate of the spectral radi-us of this matrix.
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