Inertia and controllability in infinite dimensions
type: Item
instance of: scholarly article
title: Inertia and controllability in infinite dimensions
zbMATH Open document ID: 0638.93011
DOI: 10.1016/0022-247X(88)90272-7
author: John W. Bunce
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: The inertia of an \(n\times n\) matrix A with complex entries is the integer triple \(In(A)=(\pi (A),v(A),\delta (A))\), where \(\pi\) (A) is the number of eigenvalues in the open right half plane, v(A) is the number of eigenvalues in the open left half plane and \(\delta\) (A) is the number of eigenvalues on the imaginary axis. There are various theorems which relate the inertia of a matrix to controllability properties and the solvability of various linear equations [see \textit{F. R. Gantmacher}, The theory of matrices, Vol. I and II, Chelsea Publ. Co. (New York 1959) (for a review of the Russian original (1953) see Zbl 0050.248); and \textit{C. T. Chen}, SIAM J. Appl. Math. 25, 158-161 (1973; Zbl 0273.15009)]. The present paper generalizes these concepts to bounded operators on a Hilbert space.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A70
Mathematics Subject Classification ID: 46C99
zbMATH DE Number: 4041703
zbMATH Keywords: Lyapunov equations
zbMATH Keywords: inertia
zbMATH Keywords: controllability
zbMATH Keywords: Hilbert space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4041703