Elsevier

Linear Algebra and its Applications

Volume 484, 1 November 2015, Pages 86-129
Linear Algebra and its Applications

On biunimodular vectors for unitary matrices

https://doi.org/10.1016/j.laa.2015.06.019Get rights and content
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Abstract

A biunimodular vector of a unitary matrix AU(n) is a vector vTnCn such that AvTn as well. Over the last 30 years, the sets of biunimodular vectors for Fourier matrices have been the object of extensive research in various areas of mathematics and applied sciences. Here, we broaden this basic harmonic analysis perspective and extend the search for biunimodular vectors to arbitrary unitary matrices. This search can be motivated in various ways. The main motivation is provided by the fact, that the existence of biunimodular vectors for an arbitrary unitary matrix allows for a natural understanding of the structure of all unitary matrices.

MSC

15A21 (05B20)

Keywords

Biunimodular vectors
Cyclic n-roots
Fourier matrix
Alternating projections
Unitary group
Hadamard matrix

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