  We enrich Baker and Bowler's theory of matroids over tracts with notions of
vectors and covectors. In the case of oriented matroids, these $F$-vectors and
$F$-covectors coincide with the usual signed vectors and signed covectors. In
the case of matroids over a field $F$, the $F$-covector set resp. $F$-vector
set of an $F$-matroid is a linear subspace of $F^E$ resp. its orthogonal
complement.
