The intersection of vector spaces: An engineering approach to the shuffle formula

The most elegant way to find the intersection space of subspaces of a vector space, i.e. their “meet”, is the direct application of the so-called “shuffle formula”, which was published in 1985 . In the present paper however, a method to find this “meet” of subspaces is described which leads to the shuffle formula in an indirect manner. In the relevant literature the shuffle formula is well defined, but it is not explicitly explained how it is generated. The aim of the present paper is to provide an easy access to the shuffle formula on the basis of elementary mathematics. The direct application of the shuffle formula gives the meet in a disguised form, of which the geometrical content, i.e. the vectors which constitute the meet, can only be extracted by further calculations. The indirect application of the shuffle formula, however, involves just these vectors and thus demystifies the shuffle formula.