Normal matrices and their principal submatrices of co-order one (Q865416)

Let \(A\) be a normal matrix, let \(\nu\) be any of its indices, and let \(A - \nu\) be the matrix obtained from \(A\) by deleting the \(\nu\)th row and column. For any eigenvalue \(\lambda\) of \(A - \nu\) the author reconstructs the eigenspace of \(A\) associated to \(\lambda\) from the eigenspace of \(A - \nu\) associated to \(\lambda\). In particular, the author studies the relation between the geometric multiplicities of the eigenvalue \(\lambda\) in \(A\), resp.\ \(A - \nu\).