On the Lyapunov and Stein equations. II.

DOI10.1016/j.laa.2007.05.001zbMath1141.15015OpenAlexW2022527905MaRDI QIDQ996286

Rita Simões, Fernando Conceição Silva

Publication date: 14 September 2007

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2007.05.001

zbMATH Keywords

Lyapunov equationHermitian matricesStein equationCayley transformcongruence classesnonderogatoryinertia of matrices

Mathematics Subject Classification ID

Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Matrix equations and identities (15A24) Canonical forms, reductions, classification (15A21)

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On the solutions of a class of tensor equations ⋮ Computational Methods for Linear Matrix Equations ⋮ Extending BiCG and BiCR methods to solve the Stein tensor equation ⋮ A computational framework of gradient flows for general linear matrix equations

Cites Work

• On the Lyapunov and Stein equations
• Some theorems on the inertia of general matrices
• The inertia of a Hermitian matrix having prescribed complementary principal submatrices
• Possible inertia combinations in the Stein and Lyapunov equations
• Inertia of the Stein transformation with respect to some nonderogatory matrices
• Inertia theorems for matrices: the semidefinite case
• A Generalization of a Theorem of Lyapunov
• Unnamed Item