# Documentation

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# ordschur

Reorder eigenvalues in Schur factorization

## Syntax

`[US,TS] = ordschur(U,T,select)[US,TS] = ordschur(U,T,keyword)[US,TS] = ordschur(U,T,clusters)`

## Description

`[US,TS] = ordschur(U,T,select)` reorders the Schur factorization `X = U*T*U'` produced by the `schur` function and returns the reordered Schur matrix `TS` and the cumulative orthogonal transformation `US` such that `X = US*TS*US'`. In this reordering, the selected cluster of eigenvalues appears in the leading (upper left) diagonal blocks of the quasitriangular Schur matrix `TS`, and the corresponding invariant subspace is spanned by the leading columns of `US`. The logical vector `select` specifies the selected cluster as `E(select)` where `E` is the vector of eigenvalues as they appear along `T`'s diagonal.

 Note   To extract `E` from `T`, use ```E = ordeig(T)```, instead of `eig`. This ensures that the eigenvalues in `E` occur in the same order as they appear on the diagonal of `TS`.

`[US,TS] = ordschur(U,T,keyword)` sets the selected cluster to include all eigenvalues in one of the following regions:

keyword

Selected Region

`'lhp'`

Left-half plane (`real(E) < 0`)

`'rhp'`

Right-half plane (`real(E) > 0`)

`'udi'`

Interior of unit disk (`abs(E) < 1`)

`'udo'`

Exterior of unit disk (`abs(E) > 1`)

`[US,TS] = ordschur(U,T,clusters)` reorders multiple clusters at once. Given a vector `clusters` of cluster indices, commensurate with `E = ordeig(T)`, and such that all eigenvalues with the same `clusters` value form one cluster, `ordschur` sorts the specified clusters in descending order along the diagonal of `TS`, the cluster with highest index appearing in the upper left corner.

## See Also

#### Introduced before R2006a

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