Two condition numbers described by Ye, Vavasis, Stewart, Todd and others have been used to study the complexity of interior point algorithms. The first one is given bv the "smallest large variable" in the optimal face of the linear programming problem, and the other bv the supreme of the norms of all the oblique projection operators on the range space of AT. The first one has the disadvantage of depending on the knowledge of the optimal partition, and the second one, depends only on the data. but does ilot use ttie structure of the linear prograinriling problem. With respect to the second one, we show that it coincides with the supreme of the norms of all the oblique projections on the null space of A, and with respect to the first one, we give a characterization that does not depend on the knowledge of the optimal partition. Later we study limiting properties of the affine scaling direction. Particularly we compute a bound for the angle between all the affine scaling directions and the cost vector. The bound is related with the characterization of the condition number given above.