 #1
 6
 3
 Homework Statement:

4.1 Show that one may express any second rank matrix as the sum of a symmetric
and an antisymmetric matrix.
 Relevant Equations:

I was able to proof that any matrix could be constructed by adding a symmetric and antisymmetric matrix:
A= A/2 + A/2 + A'/2  A'/2,
A= (A/2 + A'/2) + (A/2  A'/2), where A' is the transposed matrix. Now,
A/2 + A'/2 is symmetric, since (A/2 +A'/2)' = A'/2 + A/2 (equal) and
A/2  A'/2 is antisymmetric, since (A/2  A'/2)' =  A'/2 + A/2= (A/2  A'/2).
My trouble is being to show A must be of rank 2. Any ideas?