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Inequalities for the Eigenvalues of a Non‐Negative Definite Matrix and a Generalization
Author(s) -
Goller H.,
Krafft O.
Publication year - 1985
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19850650602
Subject(s) - eigenvalues and eigenvectors , mathematics , generalization , spectrum of a matrix , rank (graph theory) , matrix (chemical analysis) , minimax , positive definite matrix , pure mathematics , combinatorics , matrix differential equation , mathematical analysis , mathematical economics , physics , materials science , quantum mechanics , composite material , differential equation
In the first part it is shown that some known inequalities for eigenvalues, e.g. for eigenvalues of sums or products of non‐negative definite matrices, easily follow from a variant of the Courant‐Fischer minimax theorem. This variant establishes a relation between the k‐th of the ordered eigenvalues and a matrix of rank k. Furthermore, the problem of determining extremal ellipsoids which are centered at a point d ≠ 0 and which are tangential at the unit sphere is discussed as a generalized eigenvalue problem.
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