  We show that each algebraic representation of a matroid $M$ in positive
characteristic determines a matroid valuation of $M$, which we have named the
{\em Lindstr\"om valuation}. If this valuation is trivial, then a linear
representation of $M$ in characteristic $p$ can be derived from the algebraic
representation. Thus, so-called rigid matroids, which only admit trivial
valuations, are algebraic in positive characteristic $p$ if and only if they
are linear in characteristic $p$.
  To construct the Lindstr\"om valuation, we introduce new matroid
representations called flocks, and show that each algebraic representation of a
matroid induces flock representations.
