Results 51 to 60 of about 635 (110)
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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, 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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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
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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
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Twisted immanant and matrices with anticommuting entries
, 2015 This article gives a new matrix function named "twisted immanant," which can be regarded as an analogue of the immanant. This is defined for each self-conjugate partition through a "twisted" analogue of the irreducible character of the symmetric group ...
Itoh, Minoru
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, 2012 An n × n real matrix P is said to be a generalized reflection matrix if PT = P and P2 = I (where PT is the transpose of P). A matrix A ∈ Rn×n is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = P A
M. Dehghan, M. Hajarian
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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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Commutators from a hyperplane of matrices
, 2014 Denote by $M_n(K)$ the algebra of $n$ by $n$ matrices with entries in the field $K$. A theorem of Albert and Muckenhoupt states that every trace zero matrix of $M_n(K)$ can be expressed as $AB-BA$ for some pair $(A,B)$ of matrices of $M_n(K)$.
Pazzis, Clément de Seguins
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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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Some Equivalence Relations and Results over the Commutative Quaternions and Their Matrices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 In this paper, we give some equivalence relations and results over the commutative quaternions and their matrices. In this sense, consimilarity, semisimilarity, and consemisimilarity over the commutative quaternion algebra and commutative quaternion ...
Kosal Hidayet Huda, Tosun Murat
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