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 November 5th, 2015, 12:16 PM #1 Senior Member   Joined: Oct 2014 From: Complex Field Posts: 119 Thanks: 4 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? Thanks
 November 5th, 2015, 12:42 PM #2 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,433 Thanks: 105 $\displaystyle [b^{t}ab]^{t}=[(b^{t}a)b]^{t}=b^{t}(b^{t}a)^{t}=b^{t}a^{t}b=b^{t}ab$ Thanks from noobinmath
 November 5th, 2015, 11:06 PM #3 Senior Member   Joined: Oct 2014 From: Complex Field Posts: 119 Thanks: 4 Thank you
 November 6th, 2015, 06:39 AM #4 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,433 Thanks: 105 You're welcome.

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