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Bilateral polynomial equations with unimodular right-hand-side matrices

Tadeusz Kaczorek (2003)

International Journal of Applied Mathematics and Computer Science

Necessary and sufficient conditions are established for the existence of a solution to some bilateral polynomial matrix equations with unimodular right-hand-side matrices. A procedure for the computation of the solution is derived and illustrated by a numerical example. Two examples of applications of bilateral polynomial matrix equations are presented.

Block diagonalization

Jaromír J. Koliha (2001)

Mathematica Bohemica

We study block diagonalization of matrices induced by resolutions of the unit matrix into the sum of idempotent matrices. We show that the block diagonal matrices have disjoint spectra if and only if each idempotent matrix in the inducing resolution double commutes with the given matrix. Applications include a new characterization of an eigenprojection and of the Drazin inverse of a given matrix.

Block Factorization of Hankel Matrices and Euclidean Algorithm

S. Belhaj (2010)

Mathematical Modelling of Natural Phenomena

It is shown that a real Hankel matrix admits an approximate block diagonalization in which the successive transformation matrices are upper triangular Toeplitz matrices. The structure of this factorization was first fully discussed in [1]. This approach is extended to obtain the quotients and the remainders appearing in the Euclidean algorithm applied to two polynomials u(x) and v(x) of degree n and m, respectively, whith m < ...

Block matrix approximation via entropy loss function

Malwina Janiszewska, Augustyn Markiewicz, Monika Mokrzycka (2020)

Applications of Mathematics

The aim of the paper is to present a procedure for the approximation of a symmetric positive definite matrix by symmetric block partitioned matrices with structured off-diagonal blocks. The entropy loss function is chosen as approximation criterion. This procedure is applied in a simulation study of the statistical problem of covariance structure identification.

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