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