Ranks and the least-norm of the general solution to a system of quaternion matrix equations
Qing-Wen Wang,Cheng-Kun Li +1 more
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TLDR
Wang et al. as mentioned in this paper established a new expression of the general solution to the consistent system of linear quaternion matrix equations A1X1=C1, A2X2=C2, A3X1B1+A4X2B2 =C3.About:
This article is published in Linear Algebra and its Applications.The article was published on 2009-03-01 and is currently open access. It has received 138 citations till now. The article focuses on the topics: Quaternion & Moore–Penrose pseudoinverse.read more
Citations
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The general coupled matrix equations over generalized bisymmetric matrices
Mehdi Dehghan,Masoud Hajarian +1 more
TL;DR: In this paper, an iterative method to solve the generalized coupled matrix equations over generalized bisymmetric matrix groups was proposed, where the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases were solved using the conjugate gradient method.
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An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices
Mehdi Dehghan,Masoud Hajarian +1 more
TL;DR: In this paper, the generalized coupled Sylvester matrix equations over generalized bisymmetric matrix pair [X, Y ] were automatically determined by automatically determining the solvability of the generalized coupling Sylvesters matrix equations.
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Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations
TL;DR: In this paper, a generalized centro-symmetric solution pair of generalized coupled Sylvester matrix equations (GCSY) is computed using the conjugate gradient method.
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A system of real quaternion matrix equations with applications
TL;DR: In this article, the authors studied the problem of finding a (P, Q )-symmetric solution to a linear real quaternion matrix equation and provided necessary and sufficient conditions for the existence of a solution.
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Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations
TL;DR: The basic idea is to develop the conjugate gradients squared (CGS) and bi-conjugate gradient stabilized (Bi-CGSTAB) methods for obtaining matrix iterative methods for solving the Sylvester-transpose and periodicSylvester matrix equations.
References
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Equalities and Inequalities for Ranks of Matrices
TL;DR: In this paper, Equalities and Inequalities for Ranks of Matrices are discussed in the context of linear and multilinear algebras with respect to rank matrices.
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The spectral theorem in quaternions
TL;DR: An exposition of the spectral theory of normal matrices with quaternion entries is given in this article, where the quaternions are represented by a set of columns and columns.
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A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
TL;DR: In this article, the classical system of matrix equations A 1 XB 1 =C 1, A 2 XB 2 =C 2 over R, an arbitrary regular ring with identity, is considered.
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A pair of simultaneous linear matrix equations A1XB1 = C1, A2XB2 = C2 and a matrix programming problem
TL;DR: In this article, necessary and sufficient conditions are obtained for a pair of matrix equations A1XB1 = C1, A2XB2 = C2 on a general field F to have a common solution, along with the expression for a general common solution when certain conditions hold.
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Upper and lower bounds for ranks of matrix expressions using generalized inverses
TL;DR: In this paper, the maximal and minimal ranks of the matrix expression A 1 − B 1 X 1 C 1 − C 2 X 2 C 2 with respect to X 1 and X 2 are presented.
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