The novel concept of a cyclic sequence of a digraph that has precisely one factor is defined, and is used to characterize the entries of the inverse of a matrix with such a digraph. This leads to a characterization of a strongly sign-nonsingular matrix in terms of cyclic sequences. Nonsingular nearly reducible matrices are a well-known class of matrices having precisely one nonzero diagonal, an...

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

An n × n matrix is called a principally nonsingular matrix (NSmatrix) if all its principal minors are different from zero and it is called a totally nonsingular matrix (TNS-matrix) if all its minors are different from zero. In this paper, we are interested in the NS-matrix (TNSmatrix) completion problem: whether a partial NS-matrix (TNS-matrix) has a NS-matrix (TNS-matrix) completion. Here, we ...

A ray–nonsingular matrix is a square complex matrix, A, such that each complex matrix whose entries have the same arguments as the corresponding entries of A is nonsingular. Extremal properties of ray– nonsingular matrices are studied in this paper. Combinatorial and probabilistic arguments are used to prove that if the order of a ray– nonsingular matrix is at least 6, then it must contain a ze...

If A is a nonsingular M -matrix, some new upper and lower bounds on the minimum eigenvalue τ(A) of A are given. These bounds improve some results of Tian and Huang and are more accurate than Li et al. in some cases. In addition, we obtain some new bounds on the minimum eigenvalue of a nonsingular M -matrix A , which can give affirmative conclusions about whether bounds for the minimum eigenvalu...

A set of new formulae for the inverse of a block Hankel (or block Toeplitz) matrix is given. The formulae are expressed in terms of certain matrix Pad6 forms, which approximate a matrix power series associated with the block Hankel matrix. By using Frobenius-type identities between certain matrix Pad6 forms, the inversion formulae are shown to generalize the formulae of Gohberg-Heinig and, in t...

We present a test for determining if a substochastic matrix is convergent. By establishing a duality between weakly chained diagonally dominant (w.c.d.d.) Lmatrices and convergent substochastic matrices, we show that this test can be trivially extended to determine whether a weakly diagonally dominant (w.d.d.) matrix is a nonsingular M-matrix. The test’s runtime is linear in the order of the in...

Let A be a nonsingular M -matrix, and τ(A) denote its minimum eigenvalue. Shivakumar et al. [SIAM J. Matrix Anal. Appl., 17(2):298-312, 1996] presented some bounds of τ(A) when A is a weakly chained diagonally dominant M -matrix. The present paper establishes some new bounds of τ(A) for a general nonsingular M -matrix A. Numerical examples show that the results obtained are an improvement over ...

Let A be a nonsingular M -matrix, and τ(A) denote its minimum eigenvalue. Shivakumar et al. [SIAM J. Matrix Anal. Appl., 17(2):298-312, 1996] presented some bounds of τ(A) when A is a weakly chained diagonally dominant M -matrix. The present paper establishes some new bounds of τ(A) for a general nonsingular M -matrix A. Numerical examples show that the results obtained are an improvement over ...