Q. 85.0( 4 Votes )

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

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]

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