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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