)
= A′ – A    (Why )
= – (A – A′) = – C
Therefore
C = A – A′ is a skew symmetric matrix Theorem 2 Any square matrix can be expressed as the sum of a symmetric and a
skew symmetric matrix Proof Let A be a square matrix, then we can write
1
1
A
(A
A )
(A
A )
2
2
′
′
=
+
+
−
From the Theorem 1, we know that (A + A′) is a symmetric matrix and (A – A′) is
a skew symmetric matrix