Are multiplications of symmetric matrices commutative?

Subhotosh Khan said:
Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.
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but it is not related to my work, it is just a general yes and no question. To clarify for myself.
 
solitude said:
Are multiplications of symmetric matrices commutative?
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solitude said:
but it is not related to my work, it is just a general yes and no question. To clarify for myself.
Click to expand...
That doesn't mean you can't do some work (or have some thoughts)!

Have you tried experimenting with some symmetric matrices to see whether they commute? That's a better way to really learn something than just being told the answer.

Or, have you tried searching for properties of symmetric matrices? If they commute, that should certainly be mentioned.
 
What is the definition of a symmetric matrix?
Form two symmetric matrices (start with 2x2).
Multiply them together both ways.
Are the products equal?
Can you generalise?
 
Consider two n x n symmetric matrices A and B. Then
[math]C = AB \implies C_{ik} = \sum_{j = 1}^n A_{ij}B_{jk}[/math]
What does it mean for A and B to be symmetric? Is C symmetric? What do these statements do to the sum?

-Dan
 
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