express matrix A as a skew symmetric and symmetric matrix

Question

express matrix 'A' as a skew symmetric and symmetric matrix

Answer 1

If A is a general square matrix, it can be written as

 

A =  S  + V     where

 

S ≡  (A^T + A) /2   and

 

V  ≡  (-A^T + A) /2

 

(T denotes transpose)

 

with these definitions  S will be a  symmetric matrix and  V will be a  skew symmetric matrix.

 

For the 3 x 3 case,   S can have the meaning of a second rank tensor and the components of V can have the meaning of an axial vector.