Skew Symmetric Matrices ( Square Matrix )
Solution :
Skew Symmetric Matrices ( Square Matrix )
A square matrix A = [ aij ] is said to be skew symmetric matrix if A ′ = – A , that is aji = – aij for all possible values of i and j .
Now , if we put i = j , we have aii = – aii . Therefore 2aii = 0 or aii = 0 for all i ’ s .
This means that all the diagonal elements of a skew symmetric matrix are zero .
Numerical :
Solution : Notice that aji = – aij for all possible values of i and j . Thus it is a skew symmetric matrix . Theorem 1 : For any square matrix A with real number entries , A + A ′ is a symmetric matrix and 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 . Let A be a square matrix , then we can write