Schur decomposition.

Syntax

U, T = schur(A)

U, T = schur(A, flag)

Argument

Name

Description

A

A square matrix (n-by-n); real or complex.

flag

A string; 'real' (default) or 'complex'.

Outputs

Name

Description

U

Unitary matrix.

T

Upper triangular matrix.

Example

Syntax

H = [-28      -10     -26; 

    -150     -51    -155;

     538     181     547;];

U,T  = schur(H);

print("U = ", U);

print("T = ", T);

Result

U = [Matrix] 3 x 3

-0.044641  0.78892   0.61288

-0.27273   0.58056  -0.76718

0.96105   0.2014   -0.18924

T = [Matrix] 3 x 3

470.65     665.11    90.557

    0    -1.3228    0.36103

    0    -3.9104   -1.3228

Comments

The schur function computes the Schur decomposition of A defined by
T = U` * A * U where U is a unitary matrix (U`* U is identity) and the returned matrix T is a block upper triangular matrix in real Schur form. 

The elements on the main diagonal of this matrix T are 1x1 or 2x2 blocks.

If A is complex, T returned is an upper triangular matrix in complex Schur form.

By default, with a real matrix, it is a real Schur decomposition.  To force a complex decomposition, the flag complex can be added.

The Schur decomposition can usually be used to compute the eigenvalues of a square matrix.

The schur function uses LAPACK functions (dgees, zgees).

See Also:

eig