Relations between certain matrix products similar to commutativity

In this note it is shown that for certain pairs of (infinite) matrices A,B whose product is not commutative, there holds a relation AB=DA, similar to commutativity in that D is obtained from B by a very slight modification: by the deletion of some rows, or by the deletion of some rows and columns.     

Tensor products of certain modules for the generalized cartan matrix lie algebra

The outer multiplicites of tensor product decompositions are computed for the smallest Euclidean Kac-Moody Lie algebra when one of the tensor factors is a fundamental module or the p-module. Some combinatorial identities are obtained.     

Questions concerning matrix algebras and invariance of spectrum

Proceedings - Mathematical Sciences - LetA andB be unital Banach algebras withA a subalgebra ofB. Denote the algebra of alln xn matrices with entries fromA byM n (A). In this paper we prove some...     

Transcendence of certain infinite products

We prove the transcendence results for the infinite product , where Ek(x), Fk(x) are polynomials, α is an algebraic number, and r?2 is an integer. As applications, we give necessary and sufficient conditions for transcendence of and , where Fn and Ln are Fibonacci numbers and Lucas numbers respectively, and {ak}_k?0 is a sequence of algebraic numbers with log‖ak‖=o(rk).     

Duality between some linear preservers problems: the invariance of the c-numerical range, the c-numerical radius and certain matrix sets

Let C be a hermitian matrix. We show that the C-numerical range or C-numerical radius preservers are actually the dual operators of some matrix set preservers. We use the known results about the C-numerical range preservers to determine the structure of their dual operators. For the C-numerical radius preservers, we prove a structural theorem for the dual operators, and then determine their structure. This solves a problem in an earlier paper of the authors     

On certain generalized matrix norms

Two methods of generating classes of generalized matrix norms are presented. Particular norms obtained in this manner are investigated in some detail.     

On certain classes of matrix norms

Some characterizations of certain classes oi submultiplicative and/or general matrix norms are given.     

Elementary matrix reduction over certain rings

We explore elementary matrix reduction over certain rings characterized by properties related to stable range. Let R be a commutative ring. We call R locally stable if aR+bR = R??x∈R such that R∕(a+bx)R has stable range 1. We study locally stable rings and prove that every locally stable Bézout ring is an elementary divisor ring. Many known results on domains are thereby generalized.     

The Chebyshev solution of certain matrix equations

Summary The problem of approximating ann x m matrixC by matrices of the formX A+B Y whereA, B, X andY are of appropriate size is considered. The measure of error is the supremum of the absolute values of the individual entries in the error matrix. The problem is closely related to that of approximating a bivariate functionf by sums of functions of the formxh+gy wherex andg are functions of the first variable alone andh andy are functions of the second variable. An old algorithm for constructing best approximations is described, and some of the properties of its convergence are discussed.