Excluding the null vector from the domain, can the null vector be within the range of a matrix if the eigenvalues of that matrix are all non-zero?
Explanation: I have developed two matrix representations of a linear operator, one based on a power series and the second based on Laguerre Polynomials. I thought they should be equivalent, but the power series has a homogeneous solution while the Laguerre representation is triangular with the same value on all the diagonal elements, i.e. all of its eigenvalues are the same and non-zero.