Matrix calculations for Liapunov quadratic forms
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This article is published in Journal of Differential Equations.The article was published on 1966-04-01 and is currently open access. It has received 51 citations till now. The article focuses on the topics: Isotropic quadratic form & Definite quadratic form.read more
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Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory
TL;DR: This book brings together a vast body of results on matrix theory for easy reference and immediate application with hundreds of identities, inequalities, and matrix facts stated rigorously and clearly.
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Controllability, observability and the solution of AX - XB = C
TL;DR: In this paper, a closed-form finite series representation of the unique solution X of the matrix equation AX − XB=C is developed, where the image, kernel, and rank of X are related to the controllable and unobservable subspaces of the (A, C) and (C, B) pairs respectively.
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Projection methods for large Lyapunov matrix equations
Khalide Jbilou,A. J. Riquet +1 more
TL;DR: In this article, the authors proposed Krylov subspace methods for solving large Lyapunov matrix equations of the form AX+XAT+BBT = 0, where A and B are real n× n and n× s matrices, respectively, with s ≥ n.
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Explicit formulae for the Bures metric
TL;DR: In this article, the authors derived explicit formulae for the computation of the Riemannian Bures metric g on the manifold of (finite-dimensional) nonsingular density matrices.
References
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Journal ArticleDOI
Stability by Liapunov's Direct Method With Applications
Solomon Lefschetz,R. C. Alverson +1 more
TL;DR: This invention relates to a compact integrated beacon antenna polarization switch which provides a dual polarization radiating aperture having identical radiation beacon patterns for vertical and horizontal polarization and a ferrite mode switch capable of switching between the vertical, horizontal, right and left circular radiating mode.
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Uber die Anwendung der Methode von Ljapunov auf Differenzengleichungen
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Expansion of determinantal equations into polynomial form
TL;DR: In this paper, three basic techniques for solving determinantal equations must be considered: (1) direct solution of the equation by numerical methods [l], (2-6] (directly applicable only to the case | A − A| = 0), (3) expansion into polynomial form [6-14] and (4) standard methods.