On the nonsingular symmetric factors of a real matrix
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For a given real square matrix A, the authors describes the following matrices: (∗) all nonsingular real symmetric (r.s.) matrices S such that A = S−1T for some symmetric matrix T.About:
This article is published in Linear Algebra and its Applications.The article was published on 1974-08-01 and is currently open access. It has received 7 citations till now. The article focuses on the topics: Involutory matrix & Symmetric matrix.read more
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A canonical form for a pair of real symmetric matrices that generate a nonsingular pencil
TL;DR: In this paper, Weierstrass et al. present a kanonische Paarform fur alle reell symmetrischen matrizenpaare, die ein regulares Buschel erzeugen.
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Inertia and eigenvalue relations between symmetrized and symmetrizing matrices for the real and the general field case
Frank Uhlig,Frank Uhlig +1 more
TL;DR: In this article, the authors studied the relation between the similarity invariants of a square matrix and the congruence invariant of its symmetric factors and obtained bounds for the elementary divisor structure of A in terms of the index or signature of one or both of its symmetry factors.
On choice of preconditioner for minimum residual methods for nonsymmetric matrices
TL;DR: The theory covers only a subset of nonsymmetric coefficient matrices and guarantees that convergence of a minimum residual method will essentially depend only on the eigenvalues of the preconditioned system, as is true in the symmetric case.
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Computing matrix symmetrizers, finally possible via the Huang and Nong algorithm
TL;DR: HuHuang and Nong as mentioned in this paper developed an iterative algorithm for solving finite-dimensional linear operator equations T(x) with applications, Linear Algebra Appl. 432 (2010), pp. 1176-1188
References
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On the similarity transformation between a matirx and its transpose.
Olga Taussky,Hans Zassenhaus +1 more
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Criteria for the reality of matrix eigenvalues
TL;DR: In this paper, it was shown that a matrix with linearly independent eigenvectors is similar to a hermitian matrix, and can consequently be transformed into its conjugate transpose by a positive definite Hermitian similarity.