Orthogonal projection decomposition of matrices and construction of fusion frames

Authors:
Jinsong Leng;Deguang Han
Affiliations:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China 610054;Department of Mathematics, University of Central Florida, Orlando, USA 32816
Venue:
Advances in Computational Mathematics
Year:
2013

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Abstract

We investigate decompositions of positive matrices as weighted sums of orthogonal projections, and apply them to the construction of fusion frames when fusion frame operators are prescribed. Examples are provided to demonstrate the simplicity and flexibility in this practical construction of fusion frames. As an application, we provide an method constructing Parseval fusion frames that are optimal for the one packet erasure problem.