ordschur

Reorders the eigenvalues in a Schur factorization.

Category: Mathematics > Linear Algebra

Syntax

[US, TS] = ordschur(U, T, select)

Description

The Schur form is not unique in the order of its diagonal entries. ordschur applies orthogonal swaps between neighbouring diagonal entries, keeping the factorization valid, to bring chosen eigenvalues to the leading positions. The leading columns of US then span an invariant subspace associated with those eigenvalues.

Input arguments

U, T

Schur factors from schur, with A = U*T*U'.

select

Logical (or 0/1) vector with one entry per eigenvalue; nonzero entries mark the ones to move to the top.

Output arguments

US, TS

Reordered factors with U*T*U' = US*TS*US'.

Example

Bringing the eigenvalue 6 to the top

T = [1 2 3; 0 4 5; 0 0 6];
[US, TS] = ordschur(eye(3), T, [0 0 1]);
diag(TS)'
disp(norm(US*TS*US' - T) < 1e-12)

ans = 1×3

    6.0000    1.0000    4.0000
   1

See also

schur ordeig ordqz eig