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Question

What is a symmetric and skew-symmetric matrix?


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Solution

Symmetric and skew symmetric matrix:

A matrix is symmetric if and only if it is equal to its transpose.

All entries above the main diagonal of a symmetric matrix are reflected into equal entries below the diagonal.

If matrix A is a symmetric matrix. Then,

A=AT

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.

If the matrix Ais a skew-symmetric matrix. Then,

A=-AT

Hence, If matrix A is a symmetric matrix. Then, A=AT and If the matrix Ais a skew-symmetric matrix. Then, A=-AT.


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