A variational principle for eigenvalues of pencils of Hermitian matrices |
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| Authors: | Paul Binding Branko Najman Qiang Ye |
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| Institution: | (1) Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., T2N 1N4 Calgary, Alberta, Canada;(2) Department of Mathematics, University of Zagreb, Bijeni ka 30, 41000 Zagreb, Croatia;(3) Department of Mathematics, University of Manitoba, R3T 2N2 Winnipeg, Manitoba, Canada |
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| Abstract: | LetH=(A, B) be a pair of HermitianN×N matrices. A complex number  is an eigenvalue ofH ifdet(A–B)=0 (we include = ifdetB=0). For nonsingularH (i.e., for which some is not an eigenvalue), we show precisely which eigenvalues can be characterized as 
k
+
=sup{inf{ *A:*B=1, S},SS
k},S
k being the set of subspaces of C
N
of codimensionk–1.Dedicated to the memory of our friend and colleague Branko NajmanResearch supported by NSERC of Canada and the I.W.Killam FoundationProfessor Najman died suddenly while this work was at its final stage. His research was supported by the Ministry of Science of CroatiaResearch supported by NSERC of Canada |
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| Keywords: | 47A56 15A18 49R05 |
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