Numerical Analysis Group Research Report NA-01/13

Eigenvalues and Pseudospectra of Rectangular Matrices

Thomas G Wright and Lloyd N Trefethen

July 2001, 21 pages

Pseudospectra of rectangular matrices vary continuously with the matrix entries, a feature that eigenvalues of rectangular matrices do not have. Some properties of eigenvalues and pseudospectra of rectangular matrices are explored, and an efficient algorithm for the computation of pseudospectra is given. Applications are given in (square) eigenvalue computation (Lanczos and Arnoldi iteration), square pseudospectra approximation, control theory (nearest uncontrollable system) and game theory.

Key words and phrases: Distance to uncontrollability, eigenvalues, rectangular matrices, pseudospectra

This paper is available as a 627312 byte gzipped PostScript file.

Further information is available about the MATLAB Pseudospectra GUI mentioned in the report.