On the symmetric solutions of linear matrix equations
TLDR
In this article, the necessary and sufficient conditions for the consistency of linear matrix equations with a symmetric condition on solutions are derived using the singular value decomposition and the generalized singular-value decomposition.About:
This article is published in Linear Algebra and its Applications.The article was published on 1990-04-01 and is currently open access. It has received 134 citations till now. The article focuses on the topics: Coefficient matrix & System of linear equations.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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Brief paper: Estimation of the disturbance structure from data using semidefinite programming and optimal weighting
TL;DR: New and simpler necessary and sufficient conditions for the uniqueness of the covariance estimates are presented and the optimal weighting to be used in the least-squares objective in the covariances estimation problem is formulated to ensure minimum variance in the estimates.
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Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
TL;DR: In this paper, the authors considered bisymmetric and centrosymmetric solutions to certain matrix equations over real quaternion algebra @? and obtained necessary and sufficient conditions for the matrix equation AX = C.
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An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB= C
Ya-Xin Peng,Xi-Yan Hu,Lei Zhang +2 more
TL;DR: By this iteration method, the solvability of the equation AXB=C over symmetric X can be determined automatically and its solution can be obtained within finite iteration steps, and its least-norm symmetric solution could be obtained by choosing a special kind of initial iteration matrix.
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An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation AXB=C
Guang-Xin Huang,Feng Yin,Ke Guo +2 more
TL;DR: In this article, an iterative method is constructed to solve the linear matrix equation AXB=C over skew-symmetric matrix X. The method can be used to determine the solvability of the equation over skew symmetric matrix.
References
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Towards a Generalized Singular Value Decomposition
TL;DR: The generalized singular value decomposition of any two matrices having the same number of columns has been studied in this paper, where a form for, and a constructive derivation of, the generalized singular values decomposition for any two vectors having columns is given.
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The Elimination Matrix: Some Lemmas and Applications
J.R. Magnus,H. Neudecker +1 more
TL;DR: In this paper, two transformation matrices are introduced, L and D, which contain zero and unit elements only, and they are used for maximum likelihood estimation of the multivariate normal distribution, the evaluation of Jacobians of transformations with symmetric or lower triangular matrix arguments, and the solution of matrix equations.
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Computing theCS decomposition of a partitioned orthonormal matrix
TL;DR: In this paper, an algorithm for simultaneously diagonalizing by orthogonal transformations the blocks of a partitioned matrix having orthonormal columns is described, and the algorithm is shown to be efficient.
Journal ArticleDOI
On the symmetric solutions of a linear matrix equation
TL;DR: In this article, a partitioned minimum-norm reflexive generalized inverse is applied to find the general symmetric solution X to the matrix equation AX=B and the dimension of the space of symmetric solutions is established.
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