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# Template:Det

The {{det}} mathematical formatting template gives either an HTML+CSS or a LaTeX formatted determinant of a matrix expression.

## Usage

{{det|matrix}}

or

{{det|matrix|format}}

where the first argument, matrix, is either

• a matrix variable (as bold roman, e.g.  A
from code {{math|'''A'''|tex = \mathbf{A}|&}}), or
• a [raw] matrix, i.e. without delimiters (e.g parentheses or square brackets) obtained via the {{matrix}} template (with the raw option as last argument);

and where the [optional] format as second argument (or first argument if matrix is omitted), is from

• htm: HTML+CSS [single line] markup (for matrix variable or  1  ×  1
matrix),
• HTM: HTML+CSS [multiline] markup,
• tex: LaTeX [single line] markup (for matrix variable or  1  ×  1
matrix),
• TEX: LaTeX [multiline] markup.

## Examples

The code {{math|{{det}}|&}} yields the text style HTML+CSS
 | · |
.

The code {{math|{{det|tex}}|$}} yields the text style LaTeX${\displaystyle \textstyle {|{\;\;\!\!\!}\cdot {\;\;\!\!\!}|}}$. The code {{math|{{det|'''A'''}}|&}} yields the text style HTML+CSS  | A | . The code {{math|{{det|\mathbf{A}|tex}}|$}} yields the text style LaTeX${\displaystyle \textstyle {|\mathbf {A} |}}$.

The code {{math|{{det}}|&&}} yields the display style HTML+CSS

 | · |

The code {{math|{{det|tex}}|$$}} yields the display style LaTeX ${\displaystyle {\begin{array}{l}\displaystyle {|{\;\;\!\!\!}\cdot {\;\;\!\!\!}|}\end{array}}}$ The code {{math|{{det|'''A'''}}|&&}} yields the display style HTML+CSS  | A | The code {{math|{{det|\mathbf{A}|tex}}|$$}} yields the display style LaTeX

${\displaystyle {\begin{array}{l}\displaystyle {|\mathbf {A} |}\end{array}}}$

For the following examples, you may prefer using {{matrix|...|det}} or {{matrix|...|det|tex}}, instead of {{det|{{matrix|...|raw}}|HTM}} or {{det|{{matrix|...|raw|tex}}|TEX}}.

The code

{{indent}}{{math|

{{op|det}} '''A'''{{sub|''n'',''n''}} {{=}} <!--

-->{{det|
{{matrix|
''a''{{sub|1,1}}      &&  ''a''{{sub|1,2}}      && {{...|cdots}}  && ''a''{{sub|1,''n''}}      \\
''a''{{sub|2,1}}      &&  ''a''{{sub|2,2}}      && {{...|cdots}}  && ''a''{{sub|2,''n''}}      \\
{{...|vdots}}         &&  {{...|vdots}}         && {{...|ddots}}  && {{...|vdots}}             \\
''a''{{sub|''n'',1}}  &&  ''a''{{sub|''n'',2}}  && {{...|cdots}}  && ''a''{{sub|''n'',''n''}}
|raw}}
|HTM}}

|&&}}


yields the display style HTML+CSS matrix determinant

det An,n =
 a1,1 a1,2 ⋯ a1,n a2,1 a2,2 ⋯ a2,n ⋮ ⋮ ⋱ ⋮ an,1 an,2 ⋯ an,n

while the code

{{indent}}{{math|

{{op|det|tex}} \mathbf{A}{{sub|''n'',''n''|tex}} {{=}} <!--

-->{{det|
{{matrix|
''a''{{sub|1,1|tex}}      &&  ''a''{{sub|1,2|tex}}      && {{...|cdots|tex}}  && ''a''{{sub|1,''n''|tex}}      \\
''a''{{sub|2,1|tex}}      &&  ''a''{{sub|2,2|tex}}      && {{...|cdots|tex}}  && ''a''{{sub|2,''n''|tex}}      \\
{{...|vdots|tex}}         &&  {{...|vdots|tex}}         && {{...|ddots|tex}}  && {{...|vdots|tex}}             \\
''a''{{sub|''n'',1|tex}}  &&  ''a''{{sub|''n'',2|tex}}  && {{...|cdots|tex}}  && ''a''{{sub|''n'',''n''|tex}}
|raw|tex}}
|TEX}}

|}}


yields the display style LaTeX matrix determinant

${\displaystyle {\begin{array}{l}\displaystyle {\operatorname {det} \,\mathbf {A} _{n,n}{\!\,\!}={\begin{vmatrix}{\begin{matrix}a_{1,1}{\!\,\!}&a_{1,2}{\!\,\!}&\cdots &a_{1,n}{\!\,\!}\\a_{2,1}{\!\,\!}&a_{2,2}{\!\,\!}&\cdots &a_{2,n}{\!\,\!}\\\vdots &\vdots &\ddots &\vdots \\a_{n,1}{\!\,\!}&a_{n,2}{\!\,\!}&\cdots &a_{n,n}{\!\,\!}\end{matrix}}\end{vmatrix}}}\end{array}}}$