Difference between revisions of "Manuals/calci/ANTISYMMETRIC"

Revision as of 11:06, 17 April 2015

MATRIX("ANTISYMMETRIC",order)

This function gives the matrix of order 3 which is satisfying the anti symmetric properties.
An antisymmetric matrix is a square matrix that satisfies the identity A=-A^(T) ,where A^(T) is the matrix transpose.
For example, A= ${\begin{bmatrix}0&-1\\1&0\\\end{bmatrix}}$
So the form of anti symmetric is ${\begin{bmatrix}0&a12&a13\\-a12&0&a23\\-a13&-a23&0\\\end{bmatrix}}$
Antisymmetric matrices are commonly called "skew symmetric matrices" or "antimetric".
So in CALCI,users can give the syntax as:
1.MATRIX("anti-symmetric")
2.MATRIX("antisymmetric")
2.MATRIX("skewsymmetric")
3.MATRIX("skew-symmetric)
Here this is case-insensitive.

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-<div style="font-size:30px">'''ANTISYMMETRIC'''</div><br/>
+<div style="font-size:30px">'''MATRIX("ANTISYMMETRIC",order)'''</div><br/>
+*<math> order </math>  is the order of the Anti diagonal matrix.
+==Description==
+*This function gives the matrix of order 3 which is satisfying the anti symmetric properties.
+*An antisymmetric matrix is a square matrix that satisfies the identity A=-A^(T)  ,where A^(T) is the matrix transpose.
+*For example, A= <math>\begin{bmatrix}
+& -1 \\
+& 0 \\
+\end{bmatrix}</math>
+*So the form of anti symmetric is  <math>\begin{bmatrix}
+& a12 & a13 \\
+-a12 & 0 &  a23 \\
+-a13 & -a23 & 0 \\
+\end{bmatrix}</math>
+*Antisymmetric matrices are commonly called "skew symmetric matrices"  or "antimetric".
+*So in CALCI,users can give the syntax as:
+*1.MATRIX("anti-symmetric")
+*2.MATRIX("antisymmetric")
+*2.MATRIX("skewsymmetric")
+*3.MATRIX("skew-symmetric)
+*Here this is case-insensitive.