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September 2nd, 2009, 06:31 PM   #1
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If A and B are symmetric, show A+B is also symmetric

Here's how the problem reads:
Let A and B be symmetric matrices.
a) Show that A+B is symmetric.
b) Show that AB is symmetric if and only if AB=BA.
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September 3rd, 2009, 07:51 AM   #2
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Re: If A and B are symmetric, show A+B is also symmetric

a) Since , and you have that . That is, is symmetric.

b) Suppose that is symmetric. Then you have that . But . Hence, .

Suppose . Since and you have that that is, is symmetric.
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