Positive definite solutions of some matrix equations
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The authors investigate some existence questions of positive semi-definite solutions for certain classes of matrix equations known as the generalized Lyapunov equations. The authors use a simple but useful lemma (Lemma 2.1) and properties of Fourier transforms to get sufficient and necessary conditions for certain equations and only sufficient for others.
positive definite matrix, Numerical Analysis, Algebra and Number Theory, Matrix equation, Matrix equations and identities, Positive definite functions in one variable harmonic analysis, positive definite solution, Lyapunov matrix equation, Positive matrices and their generalizations; cones of matrices, matrix equation, Positive definite matrix, Positive definite function, Fourier transform, Discrete Mathematics and Combinatorics, Geometry and Topology, Bochner’s theorem
positive definite matrix, Numerical Analysis, Algebra and Number Theory, Matrix equation, Matrix equations and identities, Positive definite functions in one variable harmonic analysis, positive definite solution, Lyapunov matrix equation, Positive matrices and their generalizations; cones of matrices, matrix equation, Positive definite matrix, Positive definite function, Fourier transform, Discrete Mathematics and Combinatorics, Geometry and Topology, Bochner’s theorem
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