A remark on common solutions of a pair of matrix equations.
Zhang, X. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Zhang, X. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Christos Kravvaritis (2014)
Special Matrices
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Determinant formulas for special binary circulant matrices are derived and a new open problem regarding the possible determinant values of these specific circulant matrices is stated. The ideas used for the proofs can be utilized to obtain more determinant formulas for other binary circulant matrices, too. The superiority of the proposed approach over the standard method for calculating the determinant of a general circulant matrix is demonstrated.
Minghua Lin, Harald K. Wimmer (2014)
Special Matrices
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Companion matrices of the second type are characterized by properties that involve bilinear maps.
Miroslav Fiedler, Frank J. Hall (2014)
Special Matrices
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In this paper, a new characterization of previously studied generalized complementary basic matrices is obtained. It is in terms of ranks and structure ranks of submatrices defined by certain diagonal positions. The results concern both the irreducible and general cases.
Enrique Navarro, Rafael Company, Lucas Jódar (1993)
Applicationes Mathematicae
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In this paper we consider Bessel equations of the type , where A is an nn complex matrix and X(t) is an nm matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.
Neuwirth, Erich (2002)
Séminaire Lotharingien de Combinatoire [electronic only]
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Gildea, Joe (2008)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Yatsuka Nakamura, Kunio Oniumi, Wenpai Chang (2008)
Formalized Mathematics
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In this paper the theory of invertibility of matrices of field elements (see e.g. [5], [6]) is developed. The main purpose of this article is to prove that the left invertibility and the right invertibility are equivalent for a matrix of field elements. To prove this, we introduced a special transformation of matrix to some canonical forms. Other concepts as zero vector and base vectors of field elements are also introduced as a preparation.MML identifier: MATRIX14, version: 7.9.01 4.101.1015 ...
Meenakshi, Ar., Indira, R. (2005)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Branko Malešević, Biljana Radičić (2012)
Kragujevac Journal of Mathematics
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Víctor Álvarez, José Andrés Armario, María Dolores Frau, Félix Gudiel (2015)
Open Mathematics
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An n by n skew-symmetric type (-1; 1)-matrix K =[ki;j ] has 1’s on the main diagonal and ±1’s elsewhere with ki;j =-kj;i . The largest possible determinant of such a matrix K is an interesting problem. The literature is extensive for n ≡ 0 mod 4 (skew-Hadamard matrices), but for n ≡ 2 mod 4 there are few results known for this question. In this paper we approach this problem constructing cocyclic matrices over the dihedral group of 2t elements, for t odd, which are equivalent to (-1;...