Decompositions and Guo Index for Toeplitz and Block Matrices with Generalized Discrete Fractional Transforms

Abstract

We show the reconstruction of Toeplitz matrix inverses from given columns and the inversion of conjugate-Toeplitz and Hankel matrices with the explicit inverses of CUPL-Toeplitz and Hankel matrices , cyclic displacements and decompositions of inverse matrices for CUPL Toeplitz matrices. The construction of nonnegative matrices and realization of partitioned spectra and the inverse eigenvalue problem are studied . We give the realizing Suleimanova spectra by permutative matrices, the spectra of structured matrices, block matrices and Guo’s index for block circulant matrices with circulant blocks . The comparative study of commuting matrix approaches for the discrete fractional fourier transform that based on new nearly tridiagonal commuting matrices are characterized . We also study the difference operators ,the image encryption by discrete fractional Fourier-type transforms ,by random matrices and in signal and image processing.