Eigenvalues and Eigenvectors using SageMath

$\newcommand{\R}{\mathbb R} \def\C{\mathbb{C}} \def\Q{\mathbb{Q}} \def\N{\mathbb{N}} \def\Z{\mathbb{Z}} \def\ev{\mathrm{ev}} \def\Im{\mathrm{Im}} \def\End{\mathrm{End}} \def\Aut{\mathrm{Aut}} \def\Hom{\mathrm{Hom}} \def\Iso{\mathrm{Iso}} \def\GL{\mathrm{GL}} \def\ker{\mathrm{ker }} \def\Span{\mathrm{Span}} \def\tr{\mathrm{tr}} \newcommand{\unit}{1\!\!1} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} $

Section 7.8 Eigenvalues and Eigenvectors using SageMath

The computer algebra system SageMath can compute eigenvalues and eigenvectors of a given matrix. Please do the relevant changes on this page to verify your calculations.

In the following examples QQ denotes the field of rational numbers. You may change it to RR, the field of real numbers. Numbers in brackets are rows of $A\text{.}$ You can change number of rows as well as entries of rows.

Computation of eigenvalues

Computation of eigenvectors

Computation of eigenspaces

Linear Algebra: Companion notes

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Section 7.8 Eigenvalues and Eigenvectors using SageMath