# Schur

Advanced Analysis Library Only

AnalysisLibErrType Schur (void *inputMatrix, int matrixSize, int order, void *orthogonalMatrix, void *schurMatrix, NIComplexNumber eigenvalues[]);

## Purpose

Computes the Schur decomposition of a real matrix A. Schur decomposition decomposes a real matrix as follows:
A = QSQH

where | Q is a real orthogonal matrix composed of Schur vectors.
| S is a real Schur form matrix, which is upper quasi-triangular with 1*1 and 2*2 blocks on its diagonal. The 2*2 matrix has complex conjugate eigenvalues of A.
| QH is the transpose of Q.

## Parameters

Input
Name | Type | Description
inputMatrix | numeric array | The input matrix.
matrixSize | integer | The order of inputMatrix.
order | integer | Specifies how to reorder the computed eigenvalues and corresponding Schur vectors. order must be one of the following values: None: The computed eigenvalues are not reordered. REAL_ASCENDING: Reorders the eigenvalues and corresponding Schur vectors in real part ascending order. REAL_DESCENDING: Reorders the eigenvalues and corresponding Schur vectors in real part descending order. MAG_ASCENDING: Reorders the eigenvalues and corresponding Schur vectors in magnitude ascending order. MAG_DESCENDING: Reorders the eigenvalues and corresponding Schur vectors in magnitude descending order.
Output
Name | Type | Description
orthogonalMatrix | numeric array | The orthogonal matrix Q. On input, if orthogonalMatrix = NULL, Q is not computed.
schurMatrix | numeric array | The Schur form matrix S. schurMatrix is a quasi-triangular matrix.
eigenvalues | complex number array | The eigenvalues of inputMatrix, in the same order that they appear on the diagonal of the output real Schur form schurMatrix.

## Return Value

Name | Type | Description
status | AnalysisLibErrType | A value that specifies the type of error that occurred. Refer to analysis.h for definitions of these constants.