Express the matrix as the sum of a symmetric matrix and a skew-symmetric matrix.

Question

Philoid · Accepted Answer

Given , As for a symmetric matrix A’ = A hence

A + A’ = 2A

A (Symmetric Matrix)

Similarly for a skew symmetric matrix since A’ = -A hence

A-A’ = 2A

A(Skew Symmetric Matrix)

So a matrix can be represented as a sum of a symmetric matrix P and skew symmetric matrix Q.

First, we will find the transpose of matrix A,

Now using the above formulas,

Hence A = P + Q

+ [Matrix A as the sum of P and Q]