Difference between revisions of "Manuals/calci/CENTROSYMMETRIC"
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Latest revision as of 23:43, 26 October 2015
MATRIX("CENTROSYMMETRIC",order)
- 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 (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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 |