Results 41 to 50 of about 560 (104)
A note of equivalence classes of matrices over a finite field
International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 2, Page 279-287, 1981., 1981 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
On relationships between two linear subspaces and two orthogonal projectors
Special Matrices, 2019 Sum and intersection of linear subspaces in a vector space over a field are fundamental operations in linear algebra. The purpose of this survey paper is to give a comprehensive approach to the sums and intersections of two linear subspaces and their ...
Tian Yongge
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Permutation matrices and matrix equivalence over a finite field
International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 3, Page 503-512, 1981., 1980 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
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]
, 2001 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
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Equivalence classes of matrices over a finite field
International Journal of Mathematics and Mathematical Sciences, Volume 2, Issue 3, Page 487-491, 1979., 1979 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
On the matrix equation $XA+AX^T =0$, II: Type 0-I interactions
, 2013 The matrix equation $XA + AX^T = 0$ was recently introduced by De Ter\'an and Dopico to study the dimension of congruence orbits. They reduced the study of this equation to a number of special cases, several of which have not been explicitly solved.
Chan, Alice Zhuo-Yu +3 more
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Cramer's rule for a class of coupled Sylvester commutative quaternion matrix equations
Demonstratio MathematicaIn this article, based on the real representation and Kronecker product, Cramer’s rule for a class of coupled Sylvester commutative quaternion matrix equations is studied and its expression is obtained.
Cai Xiaomin, Ke Yifen, Ma Changfeng
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On the Consimilarity of Split Quaternions and Split Quaternion Matrices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 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
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, 1993 International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 301-309, 1993.
Fortunata Liguori +2 more
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, 2008 Results on matrix canonical forms are used to give a complete description of the higher rank numerical range of matrices arising from the study of quantum error correction.
Li, Chi-Kwong, Sze, Nung-Sing
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