Symmetric and Skew-Symmetric Matrices:

Symmetric and Skew-Symmetric Matrices:

• A square matrix is symmetric if it is equal to its transpose, i.e., A = A^T.
• The diagonal elements of a symmetric matrix are always real.
• A square matrix is skew-symmetric if it is equal to the negative of its transpose, i.e., A = -A^T.
• The diagonal elements of a skew-symmetric matrix are always zero.
• The sum of a symmetric matrix and a skew-symmetric matrix is always a square matrix.

Formulas for Both

• Symmetric Matrix: $$A = A^T$$
• Skew-Symmetric Matrix: $$A = -A^T$$