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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 …