# \(\text{Schur}\)¶

You can use the \(\text{Schur}\) function to perform an Schur decomposition of a real or complex matrix, creating \(Q U Q^{-1}\) where \(Q\) is a unitary matrix, \(U\) is an upper triangular matrix, and \(Q^{-1}\) is the inverse of \(Q\).

Performs Schur decomposition

You can use the schur backslash command to insert this function.

The following variants of this function are available:

\(\text{tuple } \text{Schur} \left ( \text{<matrix>} \right )\)

The \(\text{<matrix>}\) is the square matrix to calculate the Schur decomposition of.

The \(\text{Schur}\) function returns a tuple containing:

The complex \(Q\) unitary matrix.

The complex \(U\) upper triangular matrix.

A complex column matrix holding the diagonals of the \(U\) matrix. This column matrix is also the eigenvalues of the supplied matrix.

A boolean value indicating

`true`

on success or`false`

on error.

The function is implemented internally just for complex matrices. Boolean, integer, or real matrices will be converted to a complex matrix if needed.

Figure 202 shows the basic use of the \(\text{Schur}\) function.