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.