This paper introduces a heuristic for rank minimization, which is particularly useful for nonsymmetric and non-square matrices. The heuristic involves minimizing the sum of singular values of a matrix, which is equivalent to minimizing the dual spectral norm. This approach is shown to be equivalent to minimizing the trace for symmetric and positive semidefinite matrices. The paper demonstrates that the dual spectral norm is the convex envelope of the rank function on matrices with a norm less than one, providing a relaxation of the original rank minimization problem. The method is then applied to the problem of minimum order system approximation, where the goal is to find the simplest model that meets certain performance criteria. The heuristic is formulated as a semidefinite program (SDP), which can be solved efficiently using existing software. Numerical examples are provided to illustrate the effectiveness of the heuristic.This paper introduces a heuristic for rank minimization, which is particularly useful for nonsymmetric and non-square matrices. The heuristic involves minimizing the sum of singular values of a matrix, which is equivalent to minimizing the dual spectral norm. This approach is shown to be equivalent to minimizing the trace for symmetric and positive semidefinite matrices. The paper demonstrates that the dual spectral norm is the convex envelope of the rank function on matrices with a norm less than one, providing a relaxation of the original rank minimization problem. The method is then applied to the problem of minimum order system approximation, where the goal is to find the simplest model that meets certain performance criteria. The heuristic is formulated as a semidefinite program (SDP), which can be solved efficiently using existing software. Numerical examples are provided to illustrate the effectiveness of the heuristic.