My Math Forum Why is the following matrix symmetric?

 Linear Algebra Linear Algebra Math Forum

 November 5th, 2015, 01:16 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, 01:42 PM #2 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,603 Thanks: 115 $\displaystyle [b^{t}ab]^{t}=[(b^{t}a)b]^{t}=b^{t}(b^{t}a)^{t}=b^{t}a^{t}b=b^{t}ab$ Thanks from noobinmath
 November 6th, 2015, 12:06 AM #3 Senior Member   Joined: Oct 2014 From: Complex Field Posts: 119 Thanks: 4 Thank you
 November 6th, 2015, 07:39 AM #4 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,603 Thanks: 115 You're welcome.

 Tags matrix, symmetric

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post iluvmafs Linear Algebra 3 October 25th, 2014 03:51 PM benlism Linear Algebra 1 February 17th, 2013 06:54 AM queenie_n Linear Algebra 1 November 6th, 2012 07:09 AM buttnana Linear Algebra 1 September 26th, 2011 01:55 PM BlackOps Linear Algebra 2 February 18th, 2010 09:01 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top