Any real square matrix M can be written as M = U(I + L)S, where U is a matrix of0's, l's and l's having exactly one nonzero element in each row and column, L is a strictly lower triangular matrix, and S is a {symmetric}, positivesemidefinite matrix. The aim O f this paper is to demonstrate the utility of this easily derived fact. This is done in two ways. First, the decomposition is used to dev...

Let M be an archimedean quadratic module of real t× t matrix polynomials in n variables, and let S ⊆ R be the set of all points where each element of M is positive semidefinite. Our key finding is a natural bijection between the set of pure states of M and S × P(R). This leads us to conceptual proofs of positivity certificates for matrix polynomials, including the recent seminal result of Hol a...

We study the problem of low-rank matrix completion for symmetric matrices. The minimum rank a generic partially specified depends only on location entries, and not their values, if complex entries are allowed. When required to be real, this is no longer case possible ranks called typical ranks. give combinatorial description patterns n×n matrices that have n as rank. Moreover, we describe exact...

An encryption technique is widely used to keep data confidential. Most of the block symmetric algorithms use substitution functions. Often this functions use so called S-BOX matrix. In this paper author presents one software tool for testing and measuring square s-boxes. Based of information theory functions for testing static and dynamic criteria are presented. These criterions are mathematica...

We give a matrix factorization for the solution of the linear system Ax = f , when coefficient matrix A is a dense symmetric positive definite matrix. We call this factorization as "WW T factorization". The algorithm for this factorization is given. Existence and backward error analysis of the method are given. The WDWT factorization is also presented. When the coefficient matrix is a symmetric...

Abstract We show that if X n {X_{n}} is a variety of c × {c\times n} -matrices stable under the group Sym ⁡ ( stretchy="false">[ stretchy="false">] stretchy="false">)...