# schur

Version:

Returns the Schur decomposition of a square matrix.

## Syntax

d = schur(a)
d = schur(a, option)
[c, d] = schur(a)
[c, d] = schur(a, option)

## a

Real or complex square matrix.

## option

Type of decomposition to generate. option is a string that accepts the following values.

Name Description
'complex'

Generates a complex decomposition of a.

'real'

Generates a real decomposition of a. MathScript places the real eigenvalues and complex conjugate eigenpairs on the 1-by-1 and 2-by-2 diagonal blocks of d.

## d

Block upper triangular matrix in real Schur form whose elements on the main diagonal are all 1-by-1 or 2-by-2 blocks. If a is complex, d returns an upper triangular matrix in complex Schur form.

## c

Orthogonal matrix of the same size as a. If a is complex, c returns a unitary matrix.

## Definition of schur

The Schur decomposition of a square matrix A is defined by A = CDCH, where D is a matrix in Schur form, and C H is the conjugate transpose of matrix C.

A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
[C, D] = schur(A)

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices