Jordan

The Jordan decomposition of a matrix A is a change of basis where A is written in to a diagonal or quasi-diagonal form: A equals P to the power of negative 1 end exponent J P, where P is the change of basis matrix and J is a matrix with the following structure

open parentheses table row cell lambda subscript 1 end cell 0 0 0 0 0 0 0 0 row 1 cell lambda subscript 1 end cell 0 0 0 0 0 0 0 row 0 1 cell lambda subscript 1 end cell 0 0 0 0 0 0 row 0 0 0 cell lambda subscript 2 end cell 0 0 0 0 0 row 0 0 0 1 cell lambda subscript 2 end cell 0 0 0 0 row 0 0 0 0 0 cell lambda subscript 3 end cell 0 0 0 row 0 0 0 0 0 0 down right diagonal ellipsis 0 0 row 0 0 0 0 0 0 0 cell lambda subscript n end cell 1 row 0 0 0 0 0 0 0 1 cell lambda subscript n end cell end table close parentheses

where lambda subscript 1 comma... comma lambda subscript n are the eigenvalues of A.

Syntax

jordan(Matrix)

Description

jordan(Matrix)

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

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

Related functions

Eigenvalues, Eigenvalues and eigenvectors, Diagonal matrix