Inertia theory

DOI10.1016/0024-3795(80)90196-2zbMath0441.47030OpenAlexW4205804184MaRDI QIDQ1142975

Bryan E. Cain

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1016/0024-3795(80)90196-2

zbMATH Keywords

controllabilityLyapunov's theoreminertiaSylvester's theoreminertial neutrality

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Spectrum, resolvent (47A10) Numerical range, numerical radius (47A12) General theory of linear operators (47A99) Basic linear algebra (15A99)

Related Items (13)

Inertia theorems for operator pencils and applications ⋮ Inertia and controllability in infinite dimensions ⋮ Multiplicative perturbations of stable and convergent operators ⋮ Inertia theorems for nonstationary discrete systems and dichotomy ⋮ Monotone power method in indefinite metric and inertia theorem for matrices ⋮ Some angularity and inertia theorems related to normal matrices ⋮ Stability and inertia ⋮ Unnamed Item ⋮ Monochromatic Identities for the Green Function and Uniqueness Results for Passive Imaging ⋮ An estimate for the number of eigenvalues of a Hilbert-Schmidt operator in a half-plane ⋮ Lyapunov revisited ⋮ Bezoutian and Schur-Cohn problem for operator polynomials ⋮ Stability and inertia theorems for generalized Lyapunov equations

Cites Work

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• Some theorems on the inertia of general matrices
• The inertia of a product of two hermitian matrices
• On positive semidefinite solutions of the operator Lyapunov equation
• Inertia theorems for matrices, controllability, and linear vibrations
• Matrices \(C\) with \(C^ n\to 0\)
• Spectra of products and numerical ranges
• A new criterion for H-stability of complex matrices
• Similarity and the numerical range
• Inertia theorems for matrices: the semidefinite case
• An inertia theory for operators on a Hilbert space
• Hermitian congruence for matrices with semidefinite real part and for H- stable matrices
• On the eigenvalues of A + B and AB
• A Generalization of a Theorem of Lyapunov
• A Generalization of the Inertia Theorem
• Linear Operator Equations
• The Inertial Aspects of Stein's Condition H - C ∗ HC ≫0
• Functional Operators (AM-22), Volume 2
• Fields of Values of a Matrix

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