Manuals/calci/CENTROSYMMETRIC

MATRIX("CENTROSYMMETRIC",order)

• $order$ 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 (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:

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

• 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

See Also

• ARROWHEAD
• MATRIXOPERATORS
• ANTISYMMETRIC

References

• Centro symmetric