There is also a reduced version of -theory, formula_6, defined for a compact pointed space (cf. reduced homology). This reduced theory is intuitively modulo trivial bundles. It is defined as the group of stable equivalence classes of bundles. Two bundles and are said to be stably isomorphic if there are trivial bundles formula_7 and formula_8, so that formula_9. This equivalence relation results in a group since every vector bundle can be completed to a trivial bundle by summing with its orthogonal complement. Alternatively, formula_6 can be defined as the kernel of the map formula_11 induced by the inclusion of the base point into .