# [SOLVED] Symmetric Matrix Factorizations

• Feb 1st 2010, 07:47 PM
Noxide
[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?
• Feb 1st 2010, 08:49 PM
ynj
Quote:

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.
\$\displaystyle (ABA)^T=A^TB^TA^T=ABA\$
if \$\displaystyle AB=BA,A^T=A,B^T=B\$, then \$\displaystyle (AB)^T=B^TA^T=BA=AB\$