  A series-parallel matrix is a binary matrix that can be obtained from an
empty matrix by successively adjoining rows or columns that are parallel to an
existing row/column or have at most one 1-entry. Equivalently, series-parallel
matrices are representation matrices of graphic matroids of series-parallel
graphs, which can be recognized in linear time. We propose an algorithm that,
for an m-by-n matrix A with k nonzeros, determines in expected $\mathcal{O}(m +
n + k)$ time whether A is series-parallel, or returns a minimal
non-series-parallel submatrix of A. We complement the developed algorithm by an
efficient implementation and report about computational results.
