Constructing tight fusion frames (Q629255)

A tight fusion frame is a sequence of orthogonal projection operators that sum to a scalar multiple of the identity operator. The authors resolve the question of existence of such frames in the special case where the underlying space is finite-dimensional and the fusion frame's subspaces have equal dimension. That is, they 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. The methods are completely constructive, relying on a new, flexible and elementary method for constructing unit norm tight frames.