Properties of balanced and perfect matrices

In this paper we define wheel matrices and characterize some properties of matrices that are perfect but not balanced. A consequence of our results is that if a matrixA is perfect then we can construct a polynomial number of submatricesAI,⋯,An ofA such thatA is balanced if and only if all the submatricesA1,⋯,An ofA are perfect. This implies that if the problem of testing perfection is polynomially solvable, then so is the problem of testing balancedness.