Results 11 to 20 of about 232 (79)
A Hermitian canonical form for complex matrices under consimilarity
Linear Algebra and its Applications, 1990 An algorithm is described that yields a Hermitian canonical form for complex matrices under consimilarity. It consists of three blocks corresponding to the nonnegative, negative and nonreal eigenvalues of \(A\bar A\). A similar algorithm produces a real canonical form (for complex matrices under consimilarity).
Yoopyo Hong
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A Study on Commutative Elliptic Octonion Matrices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 In this study, firstly notions of similarity and consimilarity are given for commutative elliptic octonion matrices. Then the Kalman-Yakubovich s-conjugate equation is solved for the first conjugate of commutative elliptic octonions. Also, the notions of
Sürekçi Arzu Cihan +1 more
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On the singular value decomposition of (skew-)involutory and (skew-)coninvolutory matrices
Special Matrices, 2020 The singular values σ > 1 of an n × n involutory matrix A appear in pairs (σ, 1σ{1 \over \sigma }). Their left and right singular vectors are closely connected. The case of singular values σ = 1 is discussed in detail. These singular values may appear in
Faßbender Heike, Halwaß Martin
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Similarity and Consimilarity of Elements in Real Cayley-Dickson Algebras [PDF]
, 2000 14 pages ...
Yongge Tian
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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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The Division Ring Over Conjugate Product
IEEE Access, 2019 In this paper, we investigate the rational fractions in the framework of conjugate product and establish a division ring. Some conjugate properties on the proposed division ring are obtained, and the similarity and consimilarity properties are ...
Ai-Guo Wu, Hui-Zhen Wang, Yu Teng
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Regularizing algorithm for mixed matrix pencils [PDF]
, 2017 P. Van Dooren (1979) constructed an algorithm for computing all singular summands of Kronecker’s canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability.
T. Klymchuk
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, 2014 In this paper, the consimilarity of complex matrices is generalized for the split quaternions. In this regard, coneigenvalue and coneigenvector are defined for split quaternion matrices. Also, the existence of solution to the split quaternion matrix equation X-AXB = C is characterized and the solution of the equation in the explicit form are derived ...
Hidayet Hüda Kösal +2 more
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On (con)similarities and congruences between A and A^*, A^T or A
Linear Algebra and its Applications, 2008 The complex consimilarity of complex matrices defined by \(\overline{P}^{-1} AP= B\), where \(A,B,P\in \mathbb{C}^{n\times n}\) and \(P\) is invertible, is not extensible to the quaternions since \(\overline{AB}\neq \overline{AB}\) in general. Thus, given quaternion matrices \(A,B\in \mathbb{H}^{n\times n}\), the author defines the \(j\)-conjugate of \(
J. Vermeer
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Consimilarity of quaternion matrices and complex matrices
, 2001 Liping Huang
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