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November 5th, 2015, 01:16 PM   #1
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Why is the following matrix symmetric?

If I have 2 matrices NxN so that:
A=Symmetric
B=Any matrix

Why is B(T)*A*B symmetric as well?

*(T) means transpose.

I think I should do transpose on everything, but what I get is:

(B(T)*A*B)(T)=B*A(T)*B(T)=B*A*B(T) (Because A is symmetric), but why the result I get, B*A*B(T) means that it's equal to B(T)*A*B, thus symmetric?

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November 5th, 2015, 01:42 PM   #2
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$\displaystyle [b^{t}ab]^{t}=[(b^{t}a)b]^{t}=b^{t}(b^{t}a)^{t}=b^{t}a^{t}b=b^{t}ab$
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November 6th, 2015, 12:06 AM   #3
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Thank you
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November 6th, 2015, 07:39 AM   #4
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You're welcome.
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