The defect of generalized Fourier matrices

4Citations
Citations of this article
1Readers
Mendeley users who have this article in their library.
Get full text

Abstract

The N × N complex Hadamard matrices form a real algebraic manifold CN. We have CN=MN(T)∩NUN, and following Tadej and Życzkowski we investigate here the computation of the enveloping tangent space T̃HCN=THMN(T)∩THNUN, and notably of its dimension d(H)=dim(T̃HCN), called undephased defect of H. Our main result is an explicit formula for the defect of the Fourier matrix FG associated to an arbitrary finite abelian group G=Z N1×⋯×ZNr. We also comment on the general question "does the associated quantum permutation group see the defect", with a probabilistic speculation involving Diaconis-Shahshahani type variables.

Author supplied keywords

Cite

CITATION STYLE

APA

Banica, T. (2013). The defect of generalized Fourier matrices. Linear Algebra and Its Applications, 438(9), 3667–3688. https://doi.org/10.1016/j.laa.2013.01.011

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free