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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 
$\displaystyle [b^{t}ab]^{t}=[(b^{t}a)b]^{t}=b^{t}(b^{t}a)^{t}=b^{t}a^{t}b=b^{t}ab$

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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