ELA, Volume 9, pp. 122-128, July 2002, abstract.
Isometric Tight Frames
Robert Reams and Shayne Waldron
A dxn matrix, n>=d, whose columns have equal length
and whose rows are orthonormal is constructed. This
is equivalent to finding an isometric tight frame of
n vectors in R^d (or C^d), or writing the dxd identity
matrix I = d/n \sum_{i=1}^n P_i, where the P_i are
rank 1 orthogonal projections. The simple inductive
procedure given shows that there are many such isometric
tight frames.