Results 41 to 50 of about 606 (79)
Advances on the Bessis-Moussa-Villani Trace Conjecture [PDF]
A long-standing conjecture asserts that the polynomial \[p(t) = \text{Tr}[(A+tB)^m]\] has nonnegative coefficients whenever $m$ is a positive integer and $A$ and $B$ are any two $n \times n$ positive semidefinite Hermitian matrices. The conjecture arises
Hillar, Christopher J.
core +6 more sources
A note of equivalence classes of matrices over a finite field
Let Fqm×m denote the algebra of m × m matrices over the finite field Fq of q elements, and let Ω denote a group of permutations of Fq. It is well known that each ϕϵΩ can be represented uniquely by a polynomial ϕ(x)ϵFq[x] of degree less than q; thus, the group Ω naturally determines a relation ∼ on Fqm×m as follows: if A,BϵFqm×m then A ~ B if ϕ(A) = B ...
J. V. Brawley, Gary L. Mullen
wiley +1 more source
Permutation matrices and matrix equivalence over a finite field
Let F = GF(q) denote the finite field of order q and Fm×n the ring of m × n matrices over F. Let 𝒫n be the set of all permutation matrices of order n over F so that 𝒫n is ismorphic to Sn. If Ω is a subgroup of 𝒫n and A, BϵFm×n then A is equivalent to B relative to Ω if there exists Pϵ𝒫n such that AP = B.
Gary L. Mullen
wiley +1 more source
Equivalence classes of matrices over a finite field
Let Fq = GF(q) denote the finite field of order q and F(m, q) the ring of m × m matrices over Fq. Let Ω be a group of permutations of Fq. If A, BϵF(m, q) then A is equivalent to B relative to Ω if there exists ϕϵΩ such that ϕ(A) = B where ϕ(A) is computed by substitution. Formulas are given for the number of equivalence classes of a given order and for
Gary L. Mullen
wiley +1 more source
Monotone matrix functions of successive orders [PDF]
This paper extends a result obtained by Wigner and von Neumann. We prove that a non-constant real-valued function, f(x), in C^3(I) where I is an interval of the real line, is a monotone matrix function of order n+1 on I if and only if a related, modified
Nayak, Suhas
core
On Real Solutions of the Equation Φ\u3csup\u3e\u3cem\u3et\u3c/em\u3e\u3c/sup\u3e (\u3cem\u3eA\u3c/em\u3e) = 1/\u3cem\u3en\u3c/em\u3e J\u3csub\u3e\u3cem\u3en\u3c/em\u3e\u3c/sub\u3e [PDF]
For a class of n × n-matrices, we get related real solutions to the matrix equation Φt (A) = 1/n Jn by generalizing the approach of and applying the results of Zhang, Yang, and Cao [SIAM J. Matrix Anal. Appl., 21 (1999), pp. 642–645].
Chen, Yuming
core +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 301-309, 1993.
Fortunata Liguori+2 more
wiley +1 more source
Analytical solution of a class of coupled second order differential‐difference equations
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 385-396, 1993.
L. Jódar, J. A. Martin Alustiza
wiley +1 more source
On the Consimilarity of Split Quaternions and Split Quaternion Matrices
In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In his regard, we examine the solvability conditions and general solutions of the equations and in split quaternions and split quaternion ...
Kösal Hidayet Hüda+2 more
doaj +1 more source
This paper is concerned with the numerical solutions of the general matrix equation $\sum ^{p}_{i=1}{\sum ^{s_{i}}_{j=1} }\,\,{A_{ij}X_{i}}{B_{ij}} = C$ , and the general discrete-time periodic matrix equations $\sum ^{p}_{i=1}\sum ^{s_{i}}_{j=1} (A_{i,
Basem I. Selim, Lei Du, Bo Yu
doaj +1 more source