(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am to show that the trace of the product of a symmetric and a skew-symmetric matrix is zero.Please check what I did is corect:

2. Relevant equations

3. The attempt at a solution

Let me assume:A~=A and B~=-B

(I will use # sign to denote the sum process)

trace(AB)=[#(i)](AB)_ii=[#(i)] [#(j)] a_ij*b_ji

trace(AB)=-[#(j)] [#(i)] b_ji*a_ij using conditions on A and B

=-[#(j)](AB)_jj

Since i and j are equivalent,

what we have is 2trace(AB)=0

hence,conclusion

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Skew-symmetric matrix problem

**Physics Forums | Science Articles, Homework Help, Discussion**