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

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