Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0759.15010
Hershkowitz, Daniel
Recent directions in matrix stability. (English)
[J] Linear Algebra Appl. 171, 161-186 (1992). ISSN 0024-3795

This is mainly a survey paper on matrix stability. One starts with classical stability criteria. Then one studies the present sufficient conditions for stability (with particular emphasis on $P$-matrices), the $D$-stability, the additive $D$-stability, and the Lyapunov diagonal stability.\par One discusses the weak principal submatrix rank property, shared by Lyapunov diagonally semistable matrices, the uniqueness of Lyapunov scaling factors, maximal Lyapunov scaling factors, cones of real positive semidefinite matrices and their applications to matrix stability, and inertia preserving matrices. In this context one derives some original results on stable scaling of complex matrices and on inertia preserving matrices in the acyclic case.
[M.Voicu (Iaşi)]

MSC 2000:: *15A42 Inequalities involving eigenvalues and eigenvectors
93E20 Optimal stochastic control (systems)
15A48 Positive matrices and their generalizations
15A12 Conditioning of matrices
15-02 Research monographs (linear algebra)

Keywords: matrix stability; $P$-matrices; additive $D$-stability; Lyapunov diagonal stability; weak principal submatrix rank property; Lyapunov scaling factors; cones of real positive semidefinite matrices; inertia preserving matrices; scaling

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]