Motivated by recent interest in group-symmetry in the area of semidefinite programming, we propose a numerical method for finding a finest simultaneous block-diagonalization of a finite number of symmetric matrices, or equivalently the irreducible decomposition of the matrix ∗-algebra generated by symmetric matrices. The method does not require any algebraic structure to be known in advance, wh...

Motivated by recent interest in group-symmetry in the area of semidefinite programming, we propose a numerical method for finding a finest simultaneous block-diagonalization of a finite number of symmetric matrices, or equivalently the irreducible decomposition of the matrix ∗-algebra generated by symmetric matrices. The method does not require any algebraic structure to be known in advance, wh...

Motivated by recent interest in group-symmetry in the area of semidefinite programming, we propose a numerical method for finding a finest simultaneous block-diagonalization of a finite number of symmetric matrices, or equivalently the irreducible decomposition of the matrix ∗-algebra generated by symmetric matrices. The method does not require any algebraic structure to be known in advance, wh...

A matrix lower bound is defined that generalizes ideas apparently due to S. Banach and J. von Neumann. The matrix lower bound has a natural interpretation in functional analysis, and it satisfies many of the properties that von Neumann stated for it in a restricted case. Applications for the matrix lower bound are demonstrated in several areas. In linear algebra, the matrix lower bound of a ful...

Periods of matrix power sequences in max-drast fuzzy algebra and methods of their computation are considered. Matrix power sequences occur in the theory of complex fuzzy systems with transition matrix in max-t algebra, where t is a given triangular fuzzy norm. Interpretation of a complex system in max-drast algebra reflects the situation when extreme demands are put on the reliability of the sy...

this article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. it is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...

This work formally introduces and starts investigating the structure of matrix polynomial algebra extensions a coefficient by (elementary) matrix-variables over ground ring in not necessary commuting variables. These subalgebras full rings show up noncommutative algebraic geometry. We carefully study their (one-sided or bilateral) noetherianity, obtaining precise lift Hilbert Basis Theorem when...