For matrix groups of small degree, we use an analogue of the methods used for permutation groups. We try to find some sequences of objects (subspaces and vectors) in the underlying vector space that defines a stabilizer chain which has the property that the basic orbits are not excessively large. Thus, we have a concept of a base and strong generating set (BSGS) similar to that employed in the case of permutation groups. Once such a BSGS is available, analogues of the permutation group backtrack searches for centralizer, normalizer etc may be described.