Eigenvalues and eigenvectors

This function computes the eigenvalues and eigenvectors of a matrix.

Syntax

eigenvalues_and_vectors(Matrix)
eigenvalues_and_vectors(Matrix, Field)

Description

Given a matrix, this function returns its eigenvalues and eigenvectors over normalℝ (repeated eigenvalues are not omitted). The output is a list: the odd positions correspond to eigenvalues and the even to eigenvectors. That is: at position 1 there is an eigenvalue and its associated eigenvector is in position 2, and so on.

linear_algebra.eigenvalues_and_vectors1.calc.png

Given a matrix and a field F, this functions returns its eigenvalues and eigenvectors over FLaTeXF (repeated eigenvalues are not omitted). The output is a list: the odd positions correspond to eigenvalues and the even to eigenvectors. That is: at position 1 there is an eigenvalue and its associated eigenvector is in position 2, and so on.

linear_algebra.eigenvalues_and_vectors2.calc.png