in this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. this paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (st) decomposition. by this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix s and a fuzzy triangular matrix t.

In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. This paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix S and a fuzzy triangular matrix T.

An n × n complex matrix is full ray-nonsingular if it has no zero entries and every matrix obtained by changing the magnitudes of its entries is nonsingular. It is shown that a 5×5 full ray-nonsingular matrix does not exist. This, combined with earlier results, shows that there exists an n× n full ray-nonsingular matrix if and only if n ≤ 4.

An n × n complex matrix is full ray-nonsingular if it has no zero entries and every matrix obtained by changing the magnitudes of its entries is nonsingular. It is shown that a 5×5 full ray-nonsingular matrix does not exist. This, combined with earlier results, shows that there exists an n× n full ray-nonsingular matrix if and only if n ≤ 4.

In this paper, we determine the symmetrised density of a nonsingular doubly noncentral matrix variate beta type I and II distributions under different definitions.

where P is a positive definite hermitian matrix and U is a unitary matrix. In this polar representation of the matrix A, as it is called, the two matrices P and U are unique. Since the matrix P is positive definite and nonsingular, it has the same signature as the identity matrix E while the unitary matrix U is a conjunctive automorph of E. From (1) we may deduce a somewhat similar representati...

The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of ordern in <Cxnlos'7 operations, and, hence, the inverse of any nonsingular matrix in <Cürtlog'7 operations.

The energy of a graph is the sum of the singular values of its adjacency matrix. A classic inequality for singular values of a matrix sum, including its equality case, is used to study how the energy of a graph changes when edges are removed. One sharp bound and one bound that is never sharp, for the change in graph energy when the edges of a nonsingular induced subgraph are removed, are establ...

It is the purpose of this note to point out that there may also exist bounded regions which exclude the latent roots of A. Let B: [&,-,•] be an nXn matrix with complex elements. Let (/i(l), • • ■ , n(n)) be a permutation of (1, • • • , n), and let B'\ [b'tj] be the matrix [b'v] = [&*.(,•)]. Thus£' is obtained from B by a permutation of its columns, and therefore B is nonsingular when B' is nons...

A matrix has an ordinary inverse only if it is square, and even then only if it is nonsingular or, inother words, if its columns (or rows) are linearly independent. In recent years needs have been felt innumerous areas of applied mathematics for some kind of partial inverse of a matrix that is singularor even rectangular. In this paper, some results on the Quasi-commuting inverses, are given an...