Template:Det

The following documentation is located at Template:Det/doc. [<Edit> Template:Det/doc]
[⧼Purge⧽ 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}}|$}} yields the text style LaTeX$\textstyle {|{\;\;\!\!\!}\cdot {\;\;\!\!\!}|}$.

The code {{math|{{det|'''A'''}}|&}} yields the text style HTML+CSS 

| A |

.

The code {{math|{{det|\mathbf{A}|tex}}|$}} yields the text style LaTeX$\textstyle {|\mathbf {A} |}$.

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

| · |

The code {{math|{{det|tex}}|$$}} yields the display style LaTeX

${\begin{array}{l}\displaystyle {|{\;\;\!\!\!}\cdot {\;\;\!\!\!}|}\end{array}}$

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

| A |

The code {{math|{{det|\mathbf{A}|tex}}|$$}} yields the display style LaTeX

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

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

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

See also

• {{matrix}}