Difference between revisions of "Manuals/calci/CENTROSYMMETRIC"

Revision as of 13:24, 17 April 2015

MATRIX("CENTROSYMMETRIC",order)

This function gives the matrix of order 3 which is satisfying the property of centrosymmetric.
A centrosymmetric is the square matrix which is symmetric with its center.
An n × n matrix A = [ Ai,j ] is centrosymmetric when its entries satisfy

Failed to parse (syntax error): {\displaystyle A_{i,j} = A_{n−i+1,n−j+1} for 1 \le i,j \le n } .

All 2x2 centrosymmetric matrices have the form: ${\begin{bmatrix}a&b\\b&a\\\end{bmatrix}}$
All 3×3 centrosymmetric matrices have the form:

${\begin{bmatrix}a&b&c\\d&e&d\\c&b&a\\\end{bmatrix}}$

0	-3	5	0
0	5	-3	0

@@ Line 7: / Line 7: @@
 *An n × n matrix A = [ Ai,j ] is centrosymmetric when its entries satisfy
 <math>A_{i,j} = A_{n−i+1,n−j+1} for 1 \le i,j \le n </math>.
-*All 2x2 centrosymmetric matrices have the form.....
+*All 2x2 centrosymmetric matrices have the form: <math>\begin{bmatrix}
-*All 3×3 centrosymmetric matrices have the form....
+a & b\\
+b & a \\
+\end{bmatrix}</math>
+*All 3×3 centrosymmetric matrices have the form:
+<math>\begin{bmatrix}
+a & b & c\\
+d & e & d \\
+c & b & a \\
+\end{bmatrix}</math>
 *Symmetric Toeplitz matrices are centrosymmetric.
-*Here MATRIX("centrosymmetric",5) gives centrosymmetric matrices of order 5.
+*Here MATRIX("centrosymmetric") gives centrosymmetric matrices of order 3.
+*Users can change the order of the matrix and the entries in calci.
+==Examples==
+*MATRIX("centrosymmetric")
+{| class="wikitable"
+|-
+| 80 || 15 || 58
+|-
+| -88 || -15 || -88
+|-
+| 58 || 15 || 80
+|}
+*MATRIX("centrosymmetric",4,9..15)
+{| class="wikitable"
+|-
+|-5 || 7 || 6 || -9
+|-
+|0 ||-3	|| 5 ||	0
+|-
+|0 || 5 || -3 || 0
+|-
+|-9 || 6 || 7`|| -5
+|}
+==See Also==
+*[[Manuals/calci/ARROWHEAD| ARROWHEAD]]
+*[[Manuals/calci/MATRIXOPERATORS| MATRIXOPERATORS]]
+*[[Manuals/calci/ANTISYMMETRIC| ANTISYMMETRIC]]
+==References==