Department/School

Mathematics

Date

1-1-1995

Document Type

Article

Keywords

interlacing inequalities, geometric multiplicity, principal submatrix, structured eigenvector

DOI

https://doi.org/10.1137/S0895479894266568

Abstract

"It is a straightforward matrix calculation that if λ is an eigenvalue of A, x an associated eigenvector and α the set of positions in which x has nonzero entries, then λ is also an eigenvalue of the submatrix of A that lies in the rows and columns indexed by α. A converse is presented that is the most general possible in terms of the data we use. Several corollaries are obtained by applying the main result to normal and Hermitian matrices. These corollaries lead to results concerning the case of equality in the interlacing inequalities for Hermitian matrices, and to the problem of the relationship among eigenvalue multiplicities in various principal submatrices."

Published in

SIAM Journal on Matrix Analysis and Applications

Citation/Other Information

Johnson, C.R., & Kroschel, B. K. (1995). Principal Submatrices, Geometric Multiplicities, and Structured Eigenvectors. SIAM Journal on Matrix Analysis and Applications, 16(3), 1004–1012. https://doi.org/10.1137/S0895479894266568

Included in

Mathematics Commons

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