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Eigenvalue inequalities and equalities

โœ Scribed by Roger A. Horn; Noah H. Rhee; So Wasin

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
610 KB
Volume
270
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

We consider cases of equality in three basic inequalities for eigenvalues of Hermitian matrices: Cauchy's interlacing inequalities for principal submatrices, Weyl's inequalities for sums, and the residual theorem. Several applications generalize and sharpen known results for eigenvalues of irreducible tridiagonal Hermitian matrices.

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Eigenvalue Inequalities and Schubert Cal
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โœ Uwe Helmke; Joachim Rosenthal ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 733 KB

Using techniques from algebraic topology we derive linear inequalities which relate the spectrum of a set of Hermitian matrices A I, . . . , A, E C" " " with the spectrum of the sum A + . . . + A,. These extend eigenvalue inequalities due to FREEDE-THOMPSON and HORN for sums of eigenvalues of two H