Eigenvalue Inequalities and Schubert Calculus

Uwe Helmke, Joachim Rosenthal

Type: Article

Publication Date: 1995-01-01

Citations: 52

DOI: https://doi.org/10.1002/mana.19951710113

Abstract

Abstract Using techniques from algebraic topology we derive linear inequalities which relate the spectrum of a set of Hermitian matrices A 1 ,…, A r ϵ ¢ n×n with the spectrum of the sum A 1 + … + A r . These extend eigenvalue inequalities due to Freede‐Thompson and Horn for sums of eigenvalues of two Hermitian matrices.

Locations

CiteSeer X (The Pennsylvania State University) - View - PDF
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+	Principles of Algebraic Geometry	1978	Phillip Griffiths Joseph Harris
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+	A Closed Formula for the Rule of Littlewood/Richardson with Applications in the Theory of Representations of <i>gl(V)</i> and the Superalgebra <i>pl(V)</i>	1991	Hartmut Schlosser
+	Multivariable Nyquist criteria, root loci, and pole placement: A geometric viewpoint	1981	R. Brockett C.I. Byrnes
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+ PDF Chat	New Results in Pole Assignment by Real Output Feedback	1992	Joachim Rosenthal
+ PDF Chat	An extremum property of sums of eigenvalues	1955	Helmut Wielandt
+	On the eigenvalues of sums of Hermitian matrices	1971	Robert C. Thompson Linda J. Freede
+	Spectral polyhedron of a sum of two Hermitian matrices	1982	B. V. Lidskii