# Isometric tight frames

## Robert Reams and Shayne Waldron

## Abstract:

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

## Availability: