Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

ordeig

Eigenvalues of quasitriangular matrices

Syntax

E = ordeig(T)
E = ordeig(AA,BB)

Description

E = ordeig(T) takes a quasitriangular Schur matrix T, typically produced by schur, and returns the vector E of eigenvalues in their order of appearance down the diagonal of T.

E = ordeig(AA,BB) takes a quasitriangular matrix pair AA and BB, typically produced by qz, and returns the generalized eigenvalues in their order of appearance down the diagonal of AA-λ*BB.

ordeig is an order-preserving version of eig for use with ordschur and ordqz. It is also faster than eig for quasitriangular matrices.

Examples

Example 1

T=diag([1 -1 3 -5 2]);

ordeig(T) returns the eigenvalues of T in the same order they appear on the diagonal.

ordeig(T)

ans =

     1
    -1
     3
    -5
     2

eig(T), on the other hand, returns the eigenvalues in order of increasing magnitude.

eig(T)

ans =

    -5
    -1
     1
     2
     3

Example 2

A = rand(10);
[U, T] = schur(A);
abs(ordeig(T))

ans =

    5.3786
    0.7564
    0.7564
    0.7802
    0.7080
    0.7080
    0.5855
    0.5855
    0.1445
    0.0812
% Move eigenvalues with magnitude < 0.5 to the 
% upper-left corner of T.
[U,T] = ordschur(U,T,abs(E)<0.5);
abs(ordeig(T))

ans =

    0.1445
    0.0812
    5.3786
    0.7564
    0.7564
    0.7802
    0.7080
    0.7080
    0.5855
    0.5855

See Also

| | | |

Introduced before R2006a

Was this topic helpful?