Matrix in maths

Defining with \definemathmatrix

In order to type matrices in math formulas, there is the command \definemathmatrix. Once a certain type of matrix is defined, one can also add a simple command in order to type matrices in a Matlab or Scilab format.

Here are a few examples.

\setuplayout[scale=0.8,width=13cm]

\definemathmatrix[pmatrix]        % defining matrix with parentheses
	[matrix:parentheses]
	[simplecommand=pmatrix]

\definemathmatrix[bmatrix]        % defining matrix with brackets
	[matrix:brackets]
	[simplecommand=bmatrix]
 
\definemathmatrix[determinant]    % defining determinant with bars
	[matrix:bars]
	[simplecommand=thedeterminant]


Let $A$ be the matrix
\startformula
A = \startpmatrix
       \NC 2 \NC 3 \NR
       \NC 1 \NC 2 \NR
     \stoppmatrix
\stopformula

Show that
\startformula
{\rm det}(A) = \startdeterminant
                 \NC 2 \NC 3 \NR
                 \NC 1 \NC 2 \NR
               \stopdeterminant   = 1
\stopformula

Compute the matrix $AB$ where $B$ is the matrix
\startformula
B = \pmatrix{2, -3 ; -1, 2}.
\stopformula

Formatting delimiters with left and right

It is possible to have different delimiters on the left and on the right. For instance:

\definemathmatrix[pvmatrix]
	[left={\left(\thinspace},
	right={\thinspace\right|}]
	
\definemathmatrix[rpmatrix]
	[left={\left.\thinspace},
	right={\thinspace\right]}]

\startformula
	\startpvmatrix
		\NC 11 \NC 12 \NC 13 \NR
		\NC 21 \NC 22 \NC 23 \NR
		\NC 31 \NC 32 \NC 33 \NR
	\stoppvmatrix
	\startrpmatrix
		\NC  0 \NR
		\NC  1 \NR
		\NC  2 \NR
	\stoprpmatrix
\stopformula

Block matrices with vertical and/or horizontal lines

In ConTeXt LMTX beginning version 2020-11-27, it is possible to create « block » matrices where the blocks are separated by vertical or horizontal lines (respectively \VL and \HL). For instance the above example can be typeset more easily by the following :

\definemathmatrix[mymatrix]
	[left={\left\lparent\thinspace}, % instead of the left parenthesis, one can use any other fence
	right={\thinspace\right\rparent}] % instead of the right parenthesis, one can use any other fence

\starttext
Here is $3 \times 3$ matrix with a column added to it
\startformula
	\startmymatrix
		\NC 11 \NC 12 \NC 13 \VL 0 \NR
		\NC 21 \NC 22 \NC 23 \VL 1 \NR
		\NC 31 \NC 32 \NC 33 \VL 2 \NR
	\stopmymatrix
\stopformula
Here is a block matrix:
\startformula
	\startmymatrix
		\NC A \VL  B \NR
		\HL
		\NC C \VL  D \NR
	\stopmymatrix
\stopformula

Formatting lines

The two commands \VL and \HL take an optional parameter which defines the thickness of the rule and its color. So \HL[3,red] will produce a red horizontal rule three times thicker than the default matrix rule. The rule thickness for a specific matrix is defined with the [rulethickness=] parameter of \definemathmatrix.

\definemathmatrix[mymatrix][matrix:parentheses][rulethickness=2pt]

\starttext
\startformula
	\startmymatrix
		\NC A \VL[3,green]  B \NR
		\HL[10,red]
		\NC C \VL D \NR
	\stopmymatrix
\stopformula

Formatting lines

\definemathmatrix[mymatrix][matrix:parentheses]


Weird matrix
\startformula
	\startmymatrix
		\NC A \VL B \NR
		\HL[red]
		\NC C \NC D \NR
	\stopmymatrix
\stopformula

This allows things like

\startformula
	\startmymatrix
		\NC A \VL B \NR
		\HL
		\NC \NC C \NC \NR
	\stopmymatrix
	\qquad
	\startmymatrix
		\NC A_1 \VL B_1 \NR
		\HL
		\NC \vdots \NC \vdots \NC \vdots \NR
		\HL
		\NC A_n \VL B_n \NR
	\stopmymatrix
\stopformula