motivated by an arens regularity problem, we introduce the concepts of matrix banach space and matrix banach algebra. the notion of matrix normed space in the sense of ruan is a special case of our matrix normed system. a matrix banach algebra is a matrix banach space with a completely contractive multiplication. we study the structure of matrix banach spaces and matrix banach algebras. then we...

where Idn is the n×n identity matrix in R, andA = (aij). We can’t quite invert this matrix, but we almost can. Recall that any n×nmatrixM has an adjoint matrix adj(M) such that adj(M)M = det(M)Idn. The coefficients of adj(M) are polynomials in the coefficients of M. (You’ve likely seen this in the form of a formula for M when there is an inverse.) Multiplying both sides of (1) on the left by ad...

In (1) x is an m + n vector, b is an integer m-vector, c an m + n vector, and A an m X (m + n) integer matrix containing an m X m identity matrix. A is assumed to be rearranged and partitioned into an m X m optimal basis matrix B for the noninteger problem and a collection of nonbasic columns forming the matrix N with A = (B,N). An alternative form of (1) that is useful here for geometric inter...

There are various methods for obtaining the preference vector of pair-wise comparison matrix factors. These methods can be employed when the elements of pair-wise comparison matrix are crisp while they are inefficient for fuzzy elements of pair-wise comparison matrix. In this paper, a method is proposed by which the preference vector of pair-wise comparison matrix elements can be obtained even ...

Bis-(L-tyrosinato)copper(II) was reacted with 3-(chloropropyl)-trimethoxysilane functionalized silica that has infused magnetite to yield a magnetically separable catalyst in which the copper carboxylate is covalently linked to the silica matrix through the silane linkage. The immobilized catalyst has been characterized by spectroscopic studies (such as FT-IR, EPR, Magnetic Measurement...

Let I be the 2 × 2 identity matrix, and M a 2 × 2 dilation matrix with M = 2I . First, we present the correlation of the scaling functions with dilation matrix M and 2I . Then by relating the properties of scaling functions with dilation matrix 2I to the properties of scaling functions with dilation matrix M , we give a parameterization of a class of bivariate nonseparable orthogonal symmetric ...

In this paper we study the impact of Minkowski metric matrix on a projection in the Minkowski Space M along with their basic algebraic and geometric properties.The relation between the m-projections and the Minkowski inverse of a matrix A in the minkowski space M is derived. In the remaining portion commutativity of Minkowski inverse in Minkowski Space M is analyzed in terms of m-projections as...