Skip to main content Contents Index
Calc
Prev Up Next \(\require{cancel}\newcommand{\colorlinecolor}{blue!95!black!30}
\newcommand{\bwlinecolor}{black!30}
\newcommand{\thelinecolor}{\colorlinecolor}
\newcommand{\colornamesuffix}{}
\newcommand{\linestyle}{[thick, \thelinecolor]}
\newcommand{\bbm}{\begin{bmatrix}}
\newcommand{\ebm}{\end{bmatrix}}
\newcommand{\ds}{\displaystyle}
\newcommand{\thet}{\theta}
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
\newcommand{\vnorm}[1]{\left\lVert\vec #1\right\rVert}
\newcommand{\dotp}[2]{\vec #1 \,\boldsymbol{\cdot}\, \vec #2}
\newcommand{\proj}[2]{\operatorname{proj}_{\,\vec #2}{\,\vec #1}}
\newcommand{\crossp}[2]{\vec #1 \times \vec #2}
\newcommand{\veci}{\vec i}
\newcommand{\vecj}{\vec j}
\newcommand{\veck}{\vec k}
\newcommand{\vecu}{\vec u}
\newcommand{\vecv}{\vec v}
\newcommand{\vecw}{\vec w}
\newcommand{\vecx}{\vec x}
\newcommand{\vecy}{\vec y}
\newcommand{\abs}[1]{\left\lvert #1\right\rvert}
\newcommand{\noin}{\noindent}
\newcommand{\vx}[1][]{\vec{x}_{#1}}
\newcommand{\vxp}{\vec{x}_p}
\newcommand{\vu}{\vec{u}}
\newcommand{\vvv}{\vec{v}}
\newcommand{\vy}{\vec{y}}
\newcommand{\vz}{\vec{z}}
\newcommand{\vb}{\vec{b}}
\newcommand{\vw}{\vec{w}}
\newcommand{\veone}{\vec{e}_1}
\newcommand{\vetwo}{\vec{e}_2}
\newcommand{\vethree}{\vec{e}_3}
\newcommand{\vei}{\vec{e}_i}
\newcommand{\ven}[1]{\vec{e}_{#1}}
\newcommand{\zero}{\vec{0}}
\newcommand{\arref}{\overrightarrow{\text{rref}}}
\newcommand{\tta}{A}
\newcommand{\ttb}{B}
\newcommand{\ttc}{C}
\newcommand{\ttd}{D}
\newcommand{\ttm}{M}
\newcommand{\ttx}{X}
\newcommand{\tti}{I}
\newcommand{\tty}{Y}
\newcommand{\ttp}{P}
\newcommand{\ttat}{A^T}
\newcommand{\ttbt}{B^T}
\newcommand{\ttct}{C^T}
\newcommand{\ttdt}{D^T}
\newcommand{\ttmt}{M^T}
\newcommand{\ttxt}{X^T}
\newcommand{\ttit}{I^T}
\newcommand{\ttyt}{Y^T}
\newcommand{\ttai}{A^{-1}}
\newcommand{\ttbi}{B^{-1}}
\newcommand{\ttxi}{X^{-1}}
\newcommand{\ttpi}{P^{-1}}
\newcommand{\ttaxb}{\tta\vx=\vb}
\newcommand{\ttaxo}{\tta\vx=\zero}
\newcommand{\eyetwo}{\begin{bmatrix}1\amp 0\\0\amp 1\end{bmatrix}}
\newcommand{\eyethree}{\begin{bmatrix}1\amp 0\amp 0\\0\amp 1\amp 0\\0\amp 0\amp 1\end{bmatrix}}
\newcommand{\eyefour}{\begin{bmatrix}1\amp 0\amp 0\amp 0\\0\amp 1\amp 0\amp 0\\0\amp 0\amp 1\amp 0\\0\amp 0\amp 0\amp 1\end{bmatrix}}
\newcommand{\tto}{\textbf{0}}
\newcommand{\lda}{\lambda}
\newcommand{\TT}{[\, T\, ]}
\newcommand{\R}{\mathbb{R}}
\newcommand{\bvm}{\begin{vmatrix}}
\newcommand{\evm}{\end{vmatrix}}
\newcommand{\tr}{\operatorname{tr}}
\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\,}$}}}
\)
Chapter 6 Operations on Matrices
In
Chapter 4 we learned about matrix arithmetic: adding, subtracting, and multiplying matrices, finding inverses, and multiplying by scalars. In this chapter we learn about some operations that we perform
on matrices. We can think of them as functions: you input a matrix, and you get something back. One of these operations, the transpose, will return another matrix. With the other operations, the trace and the determinant, we input matrices and get numbers in return, an idea that is different than what we have seen before.