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Eigenvalue Inequalities and Schubert Calculus
Author(s) -
Helmke Uwe,
Rosenthal Joachim
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951710113
Subject(s) - mathematics , schubert calculus , calculus (dental) , inequality , eigenvalues and eigenvectors , algebra over a field , pure mathematics , mathematical analysis , orthodontics , grassmannian , medicine , physics , quantum mechanics
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.