Jordan

The Jordan decomposition of a matrix A is a change of basis where ALaTeXA is written in to a diagonal or quasi-diagonal form: A=P-1JP, where P is the change of basis matrix and J is a matrix with the following structure

λ1000000001λ1000000001λ1000000000λ2000000001λ2000000000λ3000000000000000000λn100000001λn

where λ1,...,λn are the eigenvalues of ALaTeXA.

Syntax

jordan(Matrix)

Description

Given a matrix, returns the matrix JLaTeXJ. If the option transformation_matrix is set to true, the output is a list with JLaTeXJ and PLaTeXP.

linear_algebra.jordan1.calc.png

Options

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

Option

Description

Format

Default value

transformation_matrix

We can choose if we want the output of the transformation matrix P or not.

{transformation_matrix=true}

transformation_matrix=false

exact_computations

We can choose to perform or not exact computations.

{exact_computations=false}

true, but depends on the input