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Manuals/calci/CENTROSYMMETRIC (view source)
Revision as of 18:24, 17 April 2015
, 18:24, 17 April 2015no edit summary
*An n × n matrix A = [ Ai,j ] is centrosymmetric when its entries satisfy
*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>.
<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.
*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==