In order to control an acoustic field inside a target region, it is important to choose suitable
positions of secondary sources (loudspeakers) and sensors (control points/microphones) …

We consider the existence in arbitrary finite dimensions d of a positive operator valued
measure (POVM) comprised of d 2 rank-one operators all of whose operator inner products …

For a given class F of unit norm frames of fixed redundancy we define a Grassmannian
frame as one that minimizes the maximal correlation|〈 fk, fl〉| among all frames {fk} k∈ I∈ F …

We consider the variational problem of cross-entropy loss with n feature vectors on a unit
hypersphere in R d. We prove that when d≥ n− 1, the global minimum is given by the …

This book gives a unified introduction to the rapidly developing area of finite tight frames.
Fifteen years ago, the existence of equal-norm tight frames of n> d vectors for Rd and Cd …

The classical subject of bases in Banach spaces has taken on a new life in the modern
development of applied harmonic analysis. This textbook is a self-contained introduction to …

Tight frames, also known as general Welch-bound-equality sequences, generalize
orthonormal systems. Numerous applications-including communications, coding, and …

We clarify the mathematical structure underlying unitary t-designs. These are sets of unitary
matrices, evenly distributed in the sense that the average of any t th order polynomial over …

A classic problem is the estimation of a set of parameters from measurements collected by
only a few sensors. The number of sensors is often limited by physical or economical …

Optimal frames for erasures Page 1 Linear Algebra and its Applications 377 (2004) 31–51
www.elsevier.com/locate/laa Optimal frames for erasures Roderick B. Holmes, Vern I. Paulsen …