Constructing tight fusion frames

Tight fusion frames are an emerging concept of frame theory with applications in distributed processing and communications. However, very little has been determined about the existence of such frames. We completely resolve the question of existence in the special case where the underlying space is finite-dimensional and the fusion frame's subspaces have equal dimension. That is, we precisely determine the conditions under which there exists a set of equal-rank orthogonal projection matrices whose sum is a scalar multiple of the identity matrix. The characterizing set of requirements is very mild, and as such, these frames often exist. Our methods are completely constructive, relying on a new, flexible and elementary method for constructing unit norm tight frames.