We prove that for any A, B ∈ Rn×n such that each matrix S satisfying min(A, B) ≤ S ≤ max(A, B) is nonsingular, all four matrices A−1B, AB−1, B−1A and BA−1 are P -matrices. A practical method for generating P -matrices is drawn from this result.

By the applications of Halanay type inequality and the theory of nonsingular M-matrix, the global asymptotical stability of the disease free equilibrium of a delayed malaria transmission model is obtained when the basic reproduction number of the model is less than 1.

Recently, various Uzawa methods were proposed based on different matrix splitting for solving nonsingular saddle point problems, and the necessary and sufficient condition of the convergence for those Uzawa methods were derived. Motivated by their results, in this paper we give the semi-convergence analysis of the inexact Uzawa method which is applied to solve singular saddle point problems und...

We provide the set of left-invariant minimal unit vector fields on the semi-direct product Rn oP R, where P is a nonsingular diagonal matrix and on the 7 classes of 4-dimensional solvable Lie groups of the form R3 oP R which are unimodular and of type (R).

Recently, two distinct directions have been taken in an attempt to generalize the definition of an M-matrix. Even for nonsingular matrices, these two generalizations are not equivalent. The role of these and other classes of recently defined matrices is indicated showing their usefulness in various applications.

The Generalized Minimum Residual (GMRES) iterative method and variations of it are frequently used for solving systems of linear equations of the form Ax = b, where A is a large sparse nonsingular nonsymmetric matrix. We discuss ways to reorganize the algorithm to improve its efficiency.

computes the solution ~ x = T ?1 ~ b to a nonsingular Toeplitz or Toeplitz-like linear system T~ x = ~ b, a short displacement generator for the inverse T ?1 of T, and det T. We extend this algorithm to the similar computations with nn Cauchy (generalized Hilbert) and Cauchy-like matrices. Recursive triangular factorization of such a matrix can be computed by our algorithm at the cost of execut...

We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...

This paper introduces a novel technique for sequential blind extraction of singularly mixed sources. First, a neural-network model and an adaptive algorithm for single-source blind extraction are introduced. Next, extractability analysis is presented for singular mixing matrix, and two sets of necessary and sufficient extractability conditions are derived. The adaptive algorithm and neural-netw...