Hessenberg reduction

Performs Householder transformations since a Hessenberg matrix is obtained. A Hessenberg matrix is a matrix of the form

a11a12a13a1(n-1)a1na21a22a23a2(n-1)a2n0a32a33a3(n-1)a3n00a43a4(n-1)a4n000a5(n-1)a5n000a(n-1)(n-2)a(n-1)(n-1)a(n-1)n0000an(n-1)ann

Syntax

hessenberg_reduction(Matrix))

Description

Given a matrix, transforms it to a Hessenberg matrix.

linear_algebra.hessenberg_reduction.calc.png

Options

Below is a complete list of options that may be used in the hessenberg_reduction function.

Option

Description

Format

Default value

exact_computations

We can choose to perform or not exact computations.

{exact_computations=false}

true, but depends on the input