Difference between revisions of "Manuals/calci/ADJ"

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(Created page with "<div style="font-size:30px">'''ADJ(Array)'''</div><br/> *<math>Array</math> is the set of values. ==Description== *This function shows the Adjoint of a given matrix. *In <mat...")
 
 
(7 intermediate revisions by the same user not shown)
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*Consider3x3 matrix <math>A=\begin{pmatrix}
 
*Consider3x3 matrix <math>A=\begin{pmatrix}
 
a_{11} & a_{12} & a_{13} \\
 
a_{11} & a_{12} & a_{13} \\
c & d
+
a_{21} & a_{22} & a_{23} \\
\end{pmatrix} </math>
+
a_{31} & a_{32} & a_{33}
Its adjugate is the transpose of its cofactor matrix:adj(A)=C^T
+
\end{pmatrix} </math>.
 +
*Its adjugate is the transpose of its cofactor matrix:<math>adj(A)=C^{T} =
 +
\begin{pmatrix}
 +
+\begin{vmatrix}
 +
a_ {22}& a_{23} \\
 +
a_ {32}& a_{33}
 +
\end{vmatrix} & - \begin{vmatrix}
 +
a_ {12}& a_{13} \\
 +
a_ {32}& a_{33}
 +
\end{vmatrix} & +\begin{vmatrix}
 +
a_ {12}& a_{13} \\
 +
a_ {22}& a_{23}
 +
\end{vmatrix} \\
 +
+\begin{vmatrix}
 +
a_ {21}& a_{23} \\
 +
a_ {31}& a_{33}
 +
\end{vmatrix} & - \begin{vmatrix}
 +
a_ {11}& a_{13} \\
 +
a_ {31}& a_{33}
 +
\end{vmatrix} & +\begin{vmatrix}
 +
a_ {11}& a_{13} \\
 +
a_ {21}& a_{23}
 +
\end{vmatrix} \\
 +
+\begin{vmatrix}
 +
a_ {21}& a_{22} \\
 +
a_ {31}& a_{32}
 +
\end{vmatrix} & - \begin{vmatrix}
 +
a_ {11}& a_{12} \\
 +
a_ {31}& a_{32}
 +
\end{vmatrix} & +\begin{vmatrix}
 +
a_ {11}& a_{12} \\
 +
a_ {21}& a_{22}
 +
\end{vmatrix} \\
 +
\end{pmatrix}</math>
  
 +
==Examples==
 +
1.adj([[10,12],[-14,21]])
 +
{| class="wikitable"
 +
|-
 +
| 21 ||-12
 +
|-
 +
|14 || 10
 +
|}
 +
2.adj([[4,5,8],[3,-6,-9],[10,-12,4]])
 +
{| class="wikitable"
 +
|-
 +
| -132 ||-116||2.9999999999999982
 +
|-
 +
| -102|| -64|| 60
 +
|-
 +
| 24 || 98 || -39
 +
|}
 +
 +
3.adj([[5,-2,2,7],[1,0,0,3], [-3,1,5,0], [3,-1,-9,4]])
 +
{| class="wikitable"
 +
|-
 +
| -12 ||76||-60 ||-36
 +
|-
 +
| -56 || 207.99999999999997 || -81.99999999999999 || -57.99999999999999 ||
 +
|-
 +
| 4  || 3.999999999999999  || -1.9999999999999998  || -10 ||
 +
|-
 +
| 4 ||3.9999999999999982  || 20 || 12 ||
 +
|}
 +
 +
==Related Videos==
 +
 +
{{#ev:youtube|v=oHzpMgKuI9Q|280|center|Adjoint Matrix}}
 +
 +
==See Also==
 +
*[[Manuals/calci/MATRIXADJOINT  | MATRIXADJOINT ]]
 +
*[[Manuals/calci/MINVERSE  | MINVERSE ]]
 +
*[[Manuals/calci/MMULT  | MMULT ]]
  
 
==References==
 
==References==
 
*[https://en.wikipedia.org/wiki/Adjugate_matrix Adjugate matrix]
 
*[https://en.wikipedia.org/wiki/Adjugate_matrix Adjugate matrix]
 +
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 14:24, 9 April 2019

ADJ(Array)


  • is the set of values.

Description

  • This function shows the Adjoint of a given matrix.
  • In , is the set of matrix values.
  • Adjoint of a matrix is called adjugate, classical adjoint, or adjunct.Adjoint of a matrix formed by taking the transpose of the cofactor matrix of a given original Square matrix.
  • Adjoint of matrix A is written by .
  • The adjugate of A is the transpose of the cofactor matrix C of A, .
  • Also adjoint of a matrix is defined by .
  • The adjugate of 1x1 matrix is .
  • The adjugate of 2x2 matrix is .
  • Consider3x3 matrix .
  • Its adjugate is the transpose of its cofactor matrix:

Examples

1.adj([[10,12],[-14,21]])

21 -12
14 10

2.adj([[4,5,8],[3,-6,-9],[10,-12,4]])

-132 -116 2.9999999999999982
-102 -64 60
24 98 -39

3.adj([[5,-2,2,7],[1,0,0,3], [-3,1,5,0], [3,-1,-9,4]])

-12 76 -60 -36
-56 207.99999999999997 -81.99999999999999 -57.99999999999999
4 3.999999999999999 -1.9999999999999998 -10
4 3.9999999999999982 20 12

Related Videos

Adjoint Matrix

See Also

References