# Manuals/calci/CENTROSYMMETRIC

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

$\displaystyle A_{i,j} = A_{n−i+1,n−j+1} for 1 \le i,j \le n$ .

• 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