  We introduce a new width parameter for matroids called decomposition width
and prove that every matroid property expressible in the monadic second order
logic can be computed in linear time for matroids with bounded decomposition
width if their decomposition is given. Since decompositions of small width for
our new notion can be computed in polynomial time for matroids of bounded
branch-width represented over finite fields, our results include recent
algorithmic results of Hlineny [J. Combin. Theory Ser. B 96 (2006), 325-351] in
this area and extend his results to matroids not necessarily representable over
finite fields.
