On ranges of Lyapunov transformations

DOI10.1016/0024-3795(74)90069-XzbMath0284.15013MaRDI QIDQ1845045

Raphael Loewy, David H. Carlson

Publication date: 1974

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

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Inequalities involving eigenvalues and eigenvectors (15A42) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (21)

Sylvester and Lyapunov equations and some interpolation problems for rational matrix functions ⋮ An inertia theorem for Lyapunov's equation and the dimension of a controllability space ⋮ Applications of linear transformations to matrix equations ⋮ The Lyapunov matric equation SA+A*S=S*B*BS ⋮ On the inertia of sums of Hermitian matrices ⋮ On Ranges of Lyapunov Transformations II^† ⋮ Stability and inertia ⋮ A Semi-Definite Lyapunov Theorem and the Characterization of Tridiagonal D-Stable Matrices ⋮ Bounded groups and norm-Hermitian matrices ⋮ On the Controllability of Matrix Pairs $(A,K)$ with K Positive Semidefinite ⋮ Generalized controllability and inertia theory ⋮ Controllability and inertia theory for functions of a matrix ⋮ Nonsingular solutions of TA-BT=C ⋮ On the inertia of the Lyapunov transformAH+HA^*forH>0 ⋮ On the Routh-Hurwitz-Fujiwara and the Schur-Cohn-Fujiwara theorems for the root-separation problem ⋮ The Lyapunov order for real matrices ⋮ On the effective computation of the inertia of a non-hermitian matrix ⋮ On properties of Sylvester and Lyapunov operators ⋮ A note on stable matrices ⋮ Generalized controllability and inertia theory. II ⋮ Linear and numerical linear algebra in control theory: Some research problems

Cites Work

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• On the matrix function \(AX + X'A'\)
• Some theorems on the inertia of general matrices
• On the ranges of two functions of positive definite matrices
• Rank and inertia bounds for matrices under \(R (AH) \geq 0\)
• A remark on a theorem of Lyapunov
• A note on the matrix equation \(H=AP+PA**\)
• Inertia theorems for matrices: the semidefinite case
• A Generalization of a Theorem of Lyapunov
• On Nonnegative Solutions of the Equation $AD + DA' = - C$

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