Function: [evc, lambda, As] = vereigvec (A, x)

Verified real eigenvector of an interval matrix.

For a square interval matrix A and a real vector x, this function verifies x to be an eigenvector of some matrix in A, or not to be an eigenvector of any matrix in A, or yields no verified result (unfortunately, complex eigenvectors cannot be handled yet):

evc = 1

x is verified to be an eigenvector of some matrix in A, lambda is an interval number such that for each lambda0 ∈ lambda, A is verified to contain a matrix having (lamda0, x) as an eigenpair, As is a very tight interval matrix verified to contain a matrix having (mid (lambda), x) as an eigenpair,

evc = 0

x is verified not to be an eigenvector of any matrix in A, lambda and As consist of empty intervals,

evc = -1

no verified result (data may be wrong).

Based on the section “Real eigenvectors” in J. Rohn, A handbook of results on interval linear problems, posted at http://www.cs.cas.cz/~rohn.

This work was supported by the Czech Republic National Research Program “Information Society”, project 1ET400300415.

See also: eig.

Package: interval