Matrix Symmetry: Program to Check a Matrix Symmetry

This time I will discuss about the matrix symmetry.

Box matrix A is called symmetric if A = AT
Examples of symmetric matrices:



Theorem :
If A and B are symmetric matrices with the same size, and if k is a scalar then AT is a symmetric A + B and A - B is symmetrical kA is symmetrical (AB) T = BTAT = BA

If A is a symmetric matrix that can be in inverse, then A - 1 is a symmetric matrix.
Assume that A is a symmetric matrix and can be in the inverse, that A = AT, then:
(A − 1)T = (AT) − 1 = A − 1
Yang mana membuktikan bahwa A − 1 adalah simetris.

Produk AAT dan ATA
(AAT)T = (AT)TAT = AAT dan (ATA)T = AT(AT)T = ATA
Contoh
A adalah matriks 2 X 3
Which proves that A - 1 is symmetric.

AAT and ATA Products

(AAT) T = (AT) TAT = AAT and (ATA) T = AT (AT) T = ATA
Examples
A is the matrix 2 X 3 :


If A is a matrix that can be in inverse, then the AAT and ATA also be in inverse.

With the above understanding we can create a program to determine a metric symmetry or not. As the procedure can we make something like this:

To better understand the more there is a program that I have prepared to try using the Dev-C + +