Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598970 | Linear Algebra and its Applications | 2015 | 44 Pages |
Abstract
A biunimodular vector of a unitary matrix A∈U(n)A∈U(n) is a vector v∈Tn⊂Cnv∈Tn⊂Cn such that Av∈TnAv∈Tn 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Hartmut Führ, Ziemowit Rzeszotnik,