Abstract:
We construct a $dtimes n$ matrix, $nge d$, 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 $dtimes d$ identity matrix $I={dover n}sum_{i=1}^n P_i$, where the $P_i$ are rank $1$ orthogonal projections. %where the $P_i$ are orthogonal projections onto $1-$dimensional subspaces.