Manuals/calci/PERSYMMETRIC

MATRIX("PERSYMMETRIC",order)

• $order$ is the size of the Persymmetric matrix.

Description

• This function returns the persymmetric matrix of order 3.
• A symmetric matrix is a matrix whose values are symmetric in the northwest-to-southeast diagonal.
• If a symmetric matrix is rotated by 90°, it becomes a persymmetric matrix.
• Symmetric persymmetric matrices are sometimes called bisymmetric matrices.
• i.e., A persymmetric matrix is a square matrix which is symmetric in the northeast-to-southwest diagonal.
• The form for Persymmetric matrix of order 5x5 is:$A={\begin{bmatrix}a_{11}&a_{12}&a_{13}&a_{14}&a_{15}\\a_{21}&a_{22}&a_{23}&a_{24}&a_{14}\\a_{31}&a_{32}&a_{33}&a_{23}&a_{13}\\a_{41}&a_{42}&a_{32}&a_{22}&a_{12}\\a_{51}&a_{41}&a_{31}&a_{21}&a_{11}\end{bmatrix}}.$
• In Calci MATRIX("persymmetric") shows the matrix with the negative and positive integer values.
• MATRIX("persymmetric:boolean",5) gives the persymmetric matrix of order 5 with the values 0 and 1.

Examples

• MATRIX("persymmetric")

58	-16	48
-39	-1	-16
-49	-39	58

• MATRIX("persymmetric:integer",6)

-53	62	-80	57	-58	12
24	76	86	-29	0	-58
-15	-67	-58	-66	-29	57
-49	41	26	-58	86	-80
-78	22	41	-67	76	62
19	-78	-49	-15	24	-53

• MATRIX("persymmetric:boolean",5)

1	0	0	0	0
0	1	0	1	0
1	0	1	0	0
0	1	0	1	0
1	0	1	0	1

See Also

• SYMMETRIC
• CONFERENCE
• TRIANGULAR

References

• Persymmetric Matrix