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 = A^T
Examples of symmetric matrices:

Theorem :
If A and B are symmetric matrices with the same size, and if k is a scalar then A^T is a symmetric A + B and A - B is symmetrical kA is symmetrical (AB) ^T = B^TA^T = 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 = A^T, then:
(A ^{− 1})^T = (A^T) ^{− 1} = A ^{− 1}
Yang mana membuktikan bahwa A ^{− 1} adalah simetris.

Produk AA^T dan A^TA
(AA^T)^T = (A^T)^TA^T = AA^T dan (A^TA)^T = A^T(A^T)^T = A^TA
Contoh
A adalah matriks 2 X 3
Which proves that A ^{- 1} is symmetric.

AA^T and A^TA Products

(AA^T) ^T = (A^T) ^TA^T  =  AA^T  and (A^TA) ^T = A^T (A^T) ^T = A^TA

Examples

A is the matrix 2 X 3 : 

If A is a matrix that can be in inverse, then the AA^T and A^TA 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 + +. The program can be downloaded at ziddu.

Thank you for visiting, do not forget to comment and thumb. : D