A Matrix As A Sum Of Symmetric And Skew-Symmetric Matrices || Class 12 || Chapter 3 || Examples

In this chapter we'll be acquainted with the fundamentals of matrix and matrix algebra. Matrices is a brand new concept that you'll be studying .
Symmetric Matrix − A matrix whose transpose is equal to the matrix itself. Then it is called a symmetric matrix.Skew-symmetric matrix .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 A = 1/2 (A + A′) + 1/2 (A − A′). ... Thus, any square matrix can be expressed as the sum of a symmetric and a skew-symmetric matrix.
A matrix is symmetric if and only if it is equal to its transpose. A matrix is skew-symmetric if and only if it is the opposite of its transpose. All main diagonal entries of a skew-symmetric matrix are zero.
Symmetric matrix are those matrix whose transpose is same as original matrix. Skew symmetric matrix are those matrix, in which after transpose, -1 will has to be taken outside to attain the same matrix.