condeig

Condition numbers of the eigenvalues of a matrix.

Category: Mathematics > Linear Algebra

Syntax

c = condeig(A)

Description

The condition number of an eigenvalue is the reciprocal of the cosine of the angle between its left and right eigenvectors. It is 1 for every eigenvalue of a normal matrix (symmetric matrices are the common case) and grows as the matrix approaches one that is not diagonalizable.

This is a different measure from cond(A): a matrix can be well conditioned for inversion while some of its eigenvalues are very sensitive.

Input arguments

A

Square matrix.

Output arguments

c

Column vector; large entries mark eigenvalues that are sensitive to perturbation of A.

Example

A nearly defective matrix

A = [1 1000; 0 1.001];
condeig(A)

ans = 2×1

   1.0e+06 *

    1.0000
    1.0000

See also

eig cond balance schur