From 097f244236b682cc77c6ecf25be4150091d8daf9 Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Sun, 2 Oct 2022 03:04:14 +0000 Subject: CTAN sync 202210020304 --- info/mathtrip/src/matrix.tex | 59 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 59 insertions(+) create mode 100644 info/mathtrip/src/matrix.tex (limited to 'info/mathtrip/src/matrix.tex') diff --git a/info/mathtrip/src/matrix.tex b/info/mathtrip/src/matrix.tex new file mode 100644 index 0000000000..efd7ddb66c --- /dev/null +++ b/info/mathtrip/src/matrix.tex @@ -0,0 +1,59 @@ +%This command provides the text about matrix in the first part +%of the column 2 of the page 4. +% +%The macro has one parameter +% 1) The width allowed for the text +\newcommand\TFourMatrix[1]{% + \parbox[t]{#1}{% + \DisplaySpace{\TFourDisplaySpace}{\TFourDisplayShortSpace} + %The column is narrow, text looks better ragged right + \raggedright + + \TFourTitle{Multiplication:} + \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber} + \Fm{C = A \cdot B}, + \Fm{c_{i,j} = \sum_{k=1}^n a_{i,k} b_{k,j}}. + \end{DisplayFormulae} + + \TFourTitle{Determinants:} + $\det A \neq 0$ iff $A$ is non-singular. + \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber} + \Fm{\det A \cdot B = \det A \cdot \det B}, + \Fm{\det A = \sum_\pi \prod_{i=1}^n \sign(\pi) a_{i,\pi(i)}}. + \end{DisplayFormulae} + + \TFourTitle{$2 \times 2$ and $3 \times 3$ determinant:} + \AdjustSpace{1ex plus .5ex minus .2ex} + \begin{DisplayFormulae}{1}{0pt}{5ex plus 1ex minus 1ex}{\SmallChar}{\StyleWithoutNumber} + \Fm{\begin{bmatrix} + a &b \\ + c &d \\ + \end{bmatrix} = a d - b c} + %Second Equation, matrix 3x3 + \def\FirstPart{A=\begin{bmatrix}% + a &b &c \\ + d &e &f \\ + g &h &i \\ + \end{bmatrix}} + \FmPartA{\FirstPart = + g\begin{bmatrix}% + b &c \\ + e &f \\ + \end{bmatrix} + -h \begin{bmatrix}% + a &c \\ + d &f \\ + \end{bmatrix}+} + \FmPartB{\FirstPart =}{\enspace i \begin{bmatrix}% + a &b \\ + d &e \\ + \end{bmatrix}} + \Fm{\det A=a e i + b f g + c d h -c e g - f h a - i b d} + \end{DisplayFormulae} + + \TFourTitle{Permanents:} + \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber} + \Fm{\perm A = \sum_\pi \prod_{i=1}^n a_{i,\pi(i)}}. + \end{DisplayFormulae} + }% +} -- cgit v1.2.3