Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C

Tatiana Klimchuk; Vladimir V. Sergeichuk

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Displaying similar documents to “Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C”

Determinant evaluations for binary circulant matrices

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.

When powers of a matrix coincide with its Hadamard powers

Roman Drnovšek (2015)

Special Matrices

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We characterize matrices whose powers coincide with their Hadamard powers.

Bilinear characterizations of companion matrices

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.

A remark on common solutions of a pair of matrix equations.

Zhang, X. (2004)

Acta Mathematica Universitatis Comenianae. New Series

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Some remarks on generalized inverses of conjugate EP matrix.

Meenakshi, Ar., Indira, R. (2005)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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A New Characterization of Generalized Complementary Basic Matrices

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

Invertibility of Matrices of Field Elements

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 ...

Determinants of (–1,1)-matrices of the skew-symmetric type: a cocyclic approach

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;...

Eigenvalues and eigenvectors for the quaternion matrices of degree two.

Flaut, Cristina (2002)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Patterns with several multiple eigenvalues

J. Dorsey, C.R. Johnson, Z. Wei (2014)

Special Matrices

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Identified are certain special periodic diagonal matrices that have a predictable number of paired eigenvalues. Since certain symmetric Toeplitz matrices are special cases, those that have several multiple 5 eigenvalues are also investigated further. This work generalizes earlier work on response matrices from circularly symmetric models.

Eigenvalues of certain sparse matrices

Saleem Al-Ashhab (2013)

Matematički Vesnik

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On classical $r$ -matrix for the Kowalevski gyrostat on $so (4)$ .

Komarov, Igor V., Tsiganov, Andrey V. (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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