Computing rank, trace, and determinant

$\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\C}{\mathbb C} \newcommand{\K}{\mathbb{K}} \newcommand{\tr}{{\rm tr}} \necommand{\ker}{{\rm Ker}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} $

Section A.2 Computing rank, trace, and determinant

We use online computer algebra system SageMath ¹ to compute the rank, the trace and the determinant of a given matrix. In the following example A=matrix(RR,[[1,2,0,-1],[1,6,0,1],[1,-2,2,8]]) represents $3\times 4$ matrix $A$ over $\R\text{.}$ The entries [1,2,0,-1], [1,6,0,1], and [1,-2,2,8] represents the first, the second, and the third row of $A\text{,}$ respectively.

We can compute the rank of a matrix.

We can compute the trace of a matrix.

We can compute the determinant of a matrix.

Prev TopNext