The structure of the eigenvectors of sparse matrices
The author shows that there exists a matrix \(B\) such that if \(\lambda\) is an eigenvalue of a matrix \(A\) with algebraic multiplicity \(m\), then there are \(m\) columns of \(B\) that form a basis for the maximal invariant subspace of \(A\) associated with \(\lambda\) and such that \(\text{struct} (B)\) (this is the usual directed graph associated with the zero-nonzero pattern of \(B)\) is a subgraph of the graph obtained by adding all the edges of the form \((i,i)\) to the transitive closure of \(\text{struct} (A)\).
scientific article; zbMATH DE number 644676