schur (MathScript RT Module Function)

LabVIEW 2012 MathScript RT Module Help

Edition Date: June 2012

Part Number: 373123C-01

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Owning Class: linalgebra

Requires: MathScript RT Module

Syntax

d = schur(a)

d = schur(a, option)

[c, d] = schur(a)

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

Description

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

Examples

Inputs

Name Description
a Specifies a real or complex square matrix.
option Specifies the type of decomposition to generate. option is a string that accepts the following values.

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

Outputs

Name Description
d Returns a 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 Returns an orthogonal matrix of the same size as a. If a is complex, c returns a unitary matrix.

Details

The following table lists the support characteristics of this function.

 Supported in the LabVIEW Run-Time Engine Yes Supported on RT targets Yes Suitable for bounded execution times on RT Not characterized

Examples

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