Nomenclature Hadamard product k k2, k kF spectral norm, Frobenius norm 0l m; 0l l m zero matrix, 0l l Il; 1l m l l identity matrix, l m ones matrix

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 ...

It is well known that any nonsingular M–matrix admits an LU factorization into M–matrices (with L and U lower and upper triangular respectively) and any singular M–matrix is permutation similar to an M–matrix which admits an LU factorization into M–matrices. Varga and Cai establish necessary and sufficient conditions for a singular M–matrix (without permutation) to allow an LU factorization wit...

A simple matrix is a (0,1)-matrix with no repeated columns. For a (0,1)-matrix F , we say a (0,1)-matrix A avoids F (as a configuration) if there is no submatrix of A which is a row and column permutation of F . Let ‖A‖ denote the number of columns of A. We define forb(m,F ) = max{‖A‖ : A is an m-rowed simple matrix that avoids F}. Define an extremal matrix as an m-rowed simple matrix A with th...

This investigation deals with M/M/R/N machine repair problem with R non-reliable service stations which are subjected to unpredictable breakdown. 1here is provision of an additional server to reduce backlog in the case of heavy load of failed machines. 1he permanent service stations repair the failed machines at an identical rate m and switch to faster repair rate when all service stations are ...

Glossary Dilation matrix A 2× 2 matrix M is called a dilation matrix if all the entries of M are integers and all the eigenvalues of M are greater than one in modulus. Isotropic dilation matrix A dilation matrix M is said to be isotropic if M is similar to a diagonal matrix and all its eigenvalues have the same modulus. Wavelet system A wavelet system is a collection of square integrable functi...

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...

The pattern of a matrix M is a (0, 1)-matrix which replaces all non-zero entries of M with a 1. A directed graph is said to support M if its adjacency matrix is the pattern of M . If M is an orthogonal matrix, then a digraph which supports M must satisfy a condition known as quadrangularity. We look at quadrangularity in tournaments and determine for which orders quadrangular tournaments exist....

Abstract. A well–known property of an irreducible non–singular M–matrix is that its inverse is non–negative. However, when the matrix is an irreducible and singular M–matrix it is known that it has a generalized inverse which is non–negative, but this is not always true for any generalized inverse. We focus here in characterizing when the Moore–Penrose inverse of a symmetric, singular, irreduci...

If A and B are n× n nonsingular M -matrices, a new lower bound for the minimum eigenvalue τ(A◦B) for the Hadamard product of A and B is derived. This bound improves the result of [R. Huang. Some inequalities for the Hadamard product and the Fan product of matrices. Linear Algebra Appl., 428:1551–1559, 2008.].