Vectors of matroids over tracts

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, and in the case of ordinary matroids, they are essentially the unions of circuits resp. unions of cocircuits. 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 FE resp. its orthogonal complement.