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Structured Eigenvectors, Interlacing, And Matrix Completions, Brenda K. Kroschel
Structured Eigenvectors, Interlacing, And Matrix Completions, Brenda K. Kroschel
Dissertations, Theses, and Masters Projects
This dissertation presents results from three areas of applicable matrix analysis: structured eigenvectors, interlacing, and matrix completion problems. Although these are distinct topics, the structured eigenvector results provide connections.;It is a straightforward matrix calculation that if {dollar}\lambda{dollar} is an eigenvalue of A, x an associated structured eigenvector and {dollar}\alpha{dollar} the set of positions in which x has nonzero entries, then {dollar}\lambda{dollar} is also an eigenvalue of the submatrix of A that lies in the rows and columns indexed by {dollar}\alpha{dollar}. We present a converse to this statement and apply the results to interlacing and to matrix completion problems. Several corollaries …