4 citations · 7 across the 5 of their papers we have counts for
5 papers
Constructing all self-adjoint matrices with prescribed spectrum and diagonal
Matthew Fickus, Dustin G. Mixon, Miriam J. Poteet +1
The Schur-Horn Theorem states that there exists a self-adjoint matrix with a given spectrum and diagonal if and only if the spectrum majorizes the diagonal. Though the original pro…
Steiner equiangular tight frames
Matthew Fickus, Dustin G. Mixon, Janet C. Tremain
We provide a new method for constructing equiangular tight frames (ETFs). The construction is valid in both the real and complex settings, and shows that many of the few previously…
Auto-tuning unit norm frames
Peter G. Casazza, Matthew Fickus, Dustin G. Mixon
Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of redundant components of equal weight. They are known to be exceptionally robust against ad…
The Bourgain-Tzafriri conjecture and concrete constructions of non-pavable projections
Peter G. Casazza, Matthew Fickus, Dustin G. Mixon +1
It is known that the Kadison-Singer Problem (KS) and the Paving Conjecture (PC) are equivalent to the Bourgain-Tzafriri Conjecture (BT). Also, it is known that (PC) fails for -p…
Concrete constructions of non-pavable projections
Peter G. Casazza, Matt Fickus, Dustin Mixon +1
It is known that the paving conjecture fails for 2-paving projections with constant diagonal 1/2. But the proofs of this fact are existence proofs. We will give concrete examples o…