schtoc#

Purpose#

Reduces any 2x2 blocks on the diagonal of the real Schur matrix returned from schur(). The transformation matrix is also updated.

Format#

{ schc, transc } = schtoc(sch, trans)#

Parameters:

sch (matrix) – real NxN matrix in Real Schur form. i.e., upper triangular except for possibly 2x2 blocks on the diagonal.
trans (matrix) – real NxN matrix. the associated transformation matrix.

Returns:

schc (NxN matrix) – possibly complex, strictly upper triangular. The diagonal entries are the eigenvalues.
transc (NxN matrix) – possibly complex, the associated transformation matrix.

Examples#

 // Create a 2 x 2 matrix
 a = { 7 -2,
    12 -5 };

{ schc, transc } = schtoc(schur(a));

This example calculates the complex Schur form for a real matrix a.

Remarks#

Other than checking that the inputs are strictly real matrices, no other checks are made. If the input matrix sch is already upper triangular, it is not changed. Small off-diagonal elements are considered to be zero. See the source code for the test used.

Source#

schtoc.src