A symmetric matrix is a square matrix that is equal to its transpose.
Createing a Symmetric matrix from a square matrix is easy, just add the matrix to it’s transpose and divide by two.
Creating a Symmetric matrix from a non square matrix is done by multiplying the matrix with it’s transpose or it’s transpose with the matrix.
Transpose(A(nXm))*A (mXn)= S(nXn)
A (mXn) *Transpose(A(nXm))= S(mXm)