Journal ArticleDOI
Matrices with positive semidefinite real part
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In this paper, the authors studied positive definite matrices with the property that the real part of the matrix is positive definite, and they obtained many results in the form of inequalities.Abstract:
Matrices with the property that the real part is positive definite, have been studied for the past five decades or more. Many results in the form of inequalities have been obtained for matrices pos...read more
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Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses
TL;DR: Matrix pseudoinverses producing necessary and sufficient conditions for positive and nonnegative definiteness as discussed by the authors, and matrix pseudo-inverse producing necessary conditions for nonnegative determiniteness.
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Positive diagonal solutions to the Lyapunov equations
TL;DR: In this paper, various stability type conditions on a matrix A related to the consistency of the Lyapunov equation AD+DAt positive definite, where D is a positive diagonal matrix, are studied.
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The reverse order law revisited
TL;DR: In this article, necessary and sufficient conditions are given for the triple reverse order law (ABC) = C†B†A† to hold, and special cases are considered for some special cases.
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Matrices with positive definite Hermitian part: inequalities and linear systems
TL;DR: It is shown that the Hermitian and skew-Hermitian parts of a square matrix A are defined by the following inequality: H(A)equiv ( A + A * ) /2 and S ( A)Equiv (A - A^ * )/2.