On the eigensystems of graded matrices

Informally a graded matrix is one whose elements show a systematic decreaseor increase as one passes across the matrix. It is well known thatgraded matrices often have small eigenvalues that are determined to highrelative accuracy. Similarly, the eigenvectors can have small componentsthat are nonetheless well determined. In this paper, we give approximationsto the eigenvalues and eigenvectors of a graded matrix in terms of a basematrix that show how these phenomena come about. This...