On the Eigensystems of Graded Matrices
On the Eigensystems of Graded Matrices
Files
Publication or External Link
Date
2000-01-15
Authors
Stewart, G. W.
Advisor
Citation
DRUM DOI
Abstract
Informally a graded matrix is one whose elements show a systematic
decrease or increase as one passes across the matrix. It is well
known that graded matrices often have small eigenvalues that are
determined to high relative accuracy. Similarly, the eigenvectors can
have small components that are nonetheless well determined. In this
paper, we give approximations to the eigenvalues and eigenvectors of a
graded matrix in terms of a base matrix that show how these phenomena
come about. This approach provides condition numbers for eigenvalues
and individual components of the eigenvectors. The results are
applied to derive related results for the singular value
decomposition.
(Also cross-referenced as UMAICS-TR-2000-01)