what is symmetric matrix

A symmetric matrix is a square matrix that is equal to its transpose. Formally, AAA is symmetric if and only if A=ATA=A^TA=AT. This means that the entries of a symmetric matrix are symmetric with respect to the main diagonal, i.e., for every iii and jjj, the entry in the iiith row and jjjth column is equal to the entry in the jjjth row and iiith column. Symmetric matrices are important in various applications and have properties such as the sum and difference of two symmetric matrices being symmetric