On a class of nonsingular matrices containing B-matrices

In [3] we initiated our study of the automorphism groups of a certain class of near-rings. Specifically, let P be any complex polynomial and let P denote the near-ring of all continuous selfmaps of the complex plane where addition of functions is pointwise and the product fg of two functions f and g in P is defined by fg=f∘P∘g. The near-ring P is referred to as a laminated near-ring with laminating element P. In [3], we characterised those polynomials P(z)=anzn + an−1zn−1 +…+a0 for which Aut P is a finite group. We are able to show that Aut P is finite if and only if Deg P≧3 and ai ≠ 0 for some i ≠ 0, n. In addition, we were able to completely determine those infinite groups which occur as automorphism groups of the near-rings P. There are exactly three of them. One is GL(2) the full linear group of all real 2×2 nonsingular matrices and the other two are subgroups of GL(2). In this paper, we begin our study of the finite automorphism groups of the near-rings P. We get a result which, in contrast to the situation for the infinite automorphism groups, shows that infinitely many finite groups occur as automorphism groups of the near-rings under consideration. In addition to this and other results, we completely determine Aut P when the coefficients of P are real and Deg P = 3 or 4.

Download Full-text

Efficient generation of random nonsingular matrices

Random Structures and Algorithms ◽

10.1002/rsa.3240040108 ◽

1993 ◽

Vol 4 (1) ◽

pp. 111-118 ◽

Cited By ~ 9

Author(s):

Dana Randall

Keyword(s):

Efficient Generation ◽

Nonsingular Matrices

Download Full-text

The sparsity of Bruhat decomposition factors of nonsingular matrices

Journal of Mathematical Sciences ◽

10.1007/bf02366125 ◽

1996 ◽

Vol 79 (3) ◽

pp. 1035-1042

Author(s):

L. Yu. Kolotilina

Keyword(s):

Bruhat Decomposition ◽

Nonsingular Matrices

Download Full-text

Some singular motions of non-Abelian Toda lattices

Canadian Journal of Physics ◽

10.1139/p00-025 ◽

2000 ◽

Vol 78 (2) ◽

pp. 99-112

Author(s):

W E Couch ◽

M Surovy ◽

R J Torrence

Keyword(s):

Lattice Dynamics ◽

Wave Equations ◽

Toda Lattice ◽

Linear Wave ◽

General Solutions ◽

Wave Solutions ◽

Nonsingular Matrices ◽

Linear Wave Equations ◽

Singular Matrices ◽

Toda Lattices

Motions of finite Toda lattices are known to be associated with linear wave equations whose general solutions can be expressed in terms of progressing waves, and this association is known to generalize to finite non-Abelian Toda lattices of n x n matrices and systems of n coupled linear wave equations. We present a nontrivial family of non-Abelian Toda lattice motions that can be specialized to ones that are not finite, but not infinitely extendible either, as they contain nonvanishing but singular matrices of rank (n s). In these cases we give a natural continuation of the lattice dynamics by means of nonsingular matrices of dimension (n s) x (n s), and describe how to find s progressing wave solutions of the associated system of n coupled linear wave equations.PACS No.: 5.45-a

Download Full-text

A forbidden structure of ray nonsingular matrices

Linear Algebra and its Applications ◽

10.1016/j.laa.2013.07.015 ◽

2013 ◽

Vol 439 (8) ◽

pp. 2367-2380 ◽

Cited By ~ 3

Author(s):

Yue Liu ◽

Hai-Ying Shan

Keyword(s):

Nonsingular Matrices

Download Full-text

A New Iterative Method for Finding Approximate Inverses of Complex Matrices

Abstract and Applied Analysis ◽

10.1155/2014/563787 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

M. Kafaei Razavi ◽

A. Kerayechian ◽

M. Gachpazan ◽

S. Shateyi

Keyword(s):

Iterative Method ◽

Order Of Convergence ◽

Complex Matrices ◽

Approximate Inverse ◽

Numerical Examples ◽

Convergence Behavior ◽

Approximate Inverses ◽

Nonsingular Matrices ◽

New Iterative Method

This paper presents a new iterative method for computing the approximate inverse of nonsingular matrices. The analytical discussion of the method is included to demonstrate its convergence behavior. As a matter of fact, it is proven that the suggested scheme possesses tenth order of convergence. Finally, its performance is illustrated by numerical examples on different matrices.

Download Full-text