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...")
 
Line 20: Line 20:
 
*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}</math>
 +
a_{12} & a_{13} \\
 +
a_{21} & a_{22} & a_{23} \\
 +
a_{31} & a_{32} & a_{33}
 +
\end{pmatrix} </math>.
  
 
==References==
 
==References==
 
*[https://en.wikipedia.org/wiki/Adjugate_matrix Adjugate matrix]
 
*[https://en.wikipedia.org/wiki/Adjugate_matrix Adjugate matrix]

Revision as of 14:45, 1 June 2017

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:Failed to parse (unknown function "\begin{pmatrix}"): {\displaystyle 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}}

a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} </math>.

References