Search

Necessary and sufficient conditions for the Stieltjes moment problem to have a unique solution and for the Hamburger moment problem with the same moments to have infinitely many solutions were obtained in Hamburger's papers on the classical moment problem. In this paper, we obtain an analog of Hamburger's criterion for the matrix moment problem. [ABSTRACT FROM AUTHOR]

We show that any n × n conjugate-normal matrix can be brought by a unitary congruence transformation to block-tridiagonal form with the orders of the consecutive diagonal blocks not exceeding 1, 2, 3, ..., respectively. The proof is constructive; namely, a finite process is described that implements the reduction to the desired form. Sufficient conditions are indicated for the orders of the diagonal blocks to stabilize. In this case, the condensed form is a band matrix. [ABSTRACT FROM AUTHOR]

The article discusses the measurement of the orthogonal matrix polynomials with periodic coefficients of recurrence relations. It uses the diagonalization of the matrix transform to determine the matrices. It presents mathematical theorems that explain the problem of reconstructing the measure of a periodic sequence of coefficients.

The article discusses the proof of Thompson's determinantal inequality and tackles the conjugate transpose of a matrix or a vector X.