\(\text{Hessenberg}\)

You can use the \(\text{Hessenberg}\) function to perform a Hessenberg decomposition of a real or complex matrix, creating \(Q H Q ^ T\) or \(Q H Q^H\) respectively.

You can use the \hessenberg backslash command to insert this function.

The following variants of this function are available:

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

The \(\text{Hessenberg}\) function is implemented for real and complex matrices although the function will convert boolean and integer matrices to a real matrix, if needed.

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

  • The \(Q\) unitary matrix, and

  • The upper Hessenberg matrix, \(H\).

Figure 148 shows the basic use of the \(\text{Hessenberg}\) function.

../_images/hessenberg_example.png

Figure 148 Example Use Of The Hessenberg Function