Difference between revisions of "Manuals/calci/CENTROSYMMETRIC"
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*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" | + | *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",3) | ||
| + | {| 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== | ||
| + | *[http://en.wikipedia.org/wiki/Centrosymmetric_matrix Centro symmetric] | ||
Latest revision as of 22:43, 26 October 2015
MATRIX("CENTROSYMMETRIC",order)
- is the order of the Centro symmetric matrix.
is the order of the Centro symmetric matrix.Description
- 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:
- All 3×3 centrosymmetric matrices have the form:
- Symmetric Toeplitz matrices are centrosymmetric.
- 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",3)
| 80 | 15 | 58 |
| -88 | -15 | -88 |
| 58 | 15 | 80 |
- MATRIX("centrosymmetric",4,9..15)
| -5 | 7 | 6 | -9 |
| 0 | -3 | 5 | 0 |
| 0 | 5 | -3 | 0 |
| -9 | 6 | 7 | -5 |