Isometric tight frames

Robert Reams and Shayne Waldron


We construct a $d\times n$ matrix, $n\ge d$, 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 $d\times d$ identity matrix $I={d\over n}\sum_{i=1}^n P_i$,
where the $P_i$ are rank $1$ orthogonal projections.

Keywords: Isometric tight frame, normalised tight frame, uniform tight frame

Math Review Classification: Primary 42C15 ; Secondary 52B15, 42C40

Length: 7 pages

Last Updated: 29 May 2002

Status: To appear in the Electronic Transactions in Linear Algebra