As pattern recognition methods, subspace methods have attracted much attention in the fields of face, object and video-based recognition in recent years. In subspace methods, each instance is characterized by a subspace that is spanned by a set of vectors. Thus, the distance between instances reduces to the distance between subspaces. Herein, the subspace distance designing problem is considered mathematically. Any distance designed according the method presented here can be embedded into associated recognition algorithms. The main contributions in this paper include: – Solving the open problem proposed by Wang, Wang and Feng (2005), that is, we proved that their dissimilarity is a distance; – Presenting a general framework of subspace construction, concretely speaking, we pointed out a view that subspace distance also could be regarded as the classical distance in vector space; – Proposing two types of kernel subspace distances; – Comparing some known subspace (dis)similarities mathematically.