Isometric tight frames

Abstract

We construct a dtimesn matrix, nged, whose columns have equal length and whose rows are orthonormal. This is equivalent to finding an isometric tight frame of n vectors in Rd (or Cd), or writing the dtimesd identity matrix I=dovernsumi=1nPi, where the Pi are rank 1 orthogonal projections. %where the Pi are orthogonal projections onto 1−dimensional subspaces.