# [SOLVED] Symmetric Matrix Factorizations

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• February 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?
• February 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.
$(ABA)^T=A^TB^TA^T=ABA$
if $AB=BA,A^T=A,B^T=B$, then $(AB)^T=B^TA^T=BA=AB$