# Math Help - [SOLVED] Symmetric Matrix Factorizations

1. ## [SOLVED] Symmetric Matrix Factorizations

Class notes and textbook skim this topic. Most internet resources are too complex for my current level of knowledge.

Need a little advice on how to approach the following problems.

What I know: Symmetric Matrix <=> A^T = A

The following statements produce a symmetric matrix assuming A^T = A, and B^T = B:

A^2 - B^2 True
(A - B)(A + B) False
ABA False
ABAB False

Did I get these all correct?

Therefore the product of two symmetric matrices isn't necessarily symmetric.
What would be some conditions where they would be symmetric?

2. Originally Posted by Noxide
Class notes and textbook skim this topic. Most internet resources are too complex for my current level of knowledge.

Need a little advice on how to approach the following problems.

What I know: Symmetric Matrix <=> A^T = A

The following statements produce a symmetric matrix assuming A^T = A, and B^T = B:

A^2 - B^2 True
(A - B)(A + B) False
ABA False
ABAB False

Did I get these all correct?

Therefore the product of two symmetric matrices isn't necessarily symmetric.
What would be some conditions where they would be symmetric?
Not exactly.
$(ABA)^T=A^TB^TA^T=ABA$
if $AB=BA,A^T=A,B^T=B$, then $(AB)^T=B^TA^T=BA=AB$