## matrix A

A square real matrix.

This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.

## compute Schur vectors?

A Boolean that determines whether this node calculates the orthogonal matrix.

True |
Calculates the orthogonal matrix and the block upper triangular matrix in real Schur form. |

False |
Calculates only the block upper triangular matrix in real Schur form. |

**Default: **False

## order

Method to order the eigenvalues and the corresponding triangular matrix in real Schur form and the orthogonal matrix.

Name |
Value |
Description |

No Reorder |
0 |
Does not change the order of the eigenvalues. |

Real Ascending |
1 |
Lists the eigenvalues in ascending order according to their real parts. |

Real Descending |
2 |
Lists the eigenvalues in descending order according to their real parts. |

Magnitude Ascending |
3 |
Lists the eigenvalues in ascending order according to their magnitudes. |

Magnitude Descending |
4 |
Lists the eigenvalues in descending order according to their magnitudes. |

**Default: **No Reorder

## error in

Error conditions that occur before this node runs.
The node responds to this input according to standard error behavior.

**Default: **No error

## Schur form

The block upper triangular matrix in real Schur form.

## eigenvalues

A complex vector that contains all the computed eigenvalues of the input matrix.

## Algorithm for Calculating Schur Decomposition

The following expression defines the Schur decomposition of a square *n* × *n* matrix *A*.

*A* = *Q**S**Q*^{H}

where *S* is in Schur form and *Q*^{H} is the conjugate transpose of matrix *Q*.

For a real matrix *A*, *Q* is an *n* × *n* orthogonal matrix. *S* is a block upper triangular matrix in real Schur form, whose elements on the main diagonal are all 1 × 1 or 2 × 2 blocks, as shown in the following matrix.

$S=\left[\begin{array}{cccc}{S}_{11}& {S}_{12}& \dots & {S}_{1m}\\ 0& {S}_{22}& \ddots & {S}_{2m}\\ \vdots & \ddots & \ddots & \vdots \\ 0& 0& \dots & {S}_{mm}\end{array}\right]$

where *S*_{ii} are square blocks of dimension 1 or 2 and *i* = 1, 2, ..., *m*.

For a complex matrix *A*, *Q* is an *n* × *n* unitary matrix. *S* is an upper triangular matrix in complex Schur form.

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported