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