English

Informing the structure of complex Hadamard matrix spaces using a flow

Mathematical Physics 2016-11-02 v2 math.MP

Abstract

The defect of a complex Hadamard matrix HH is an upper bound for the dimension of a continuous Hadamard orbit stemming from HH. We provide a new interpretation of the defect as the dimension of the center subspace of a gradient flow and apply the Center Manifold Theorem of dynamical systems theory to study local structure in spaces of complex Hadamard matrices. Through examples, we provide several applications of our methodology including the construction of affine families of Hadamard matrices.

Keywords

Cite

@article{arxiv.1609.02829,
  title  = {Informing the structure of complex Hadamard matrix spaces using a flow},
  author = {Francis C. Motta and Patrick D. Shipman},
  journal= {arXiv preprint arXiv:1609.02829},
  year   = {2016}
}

Comments

17 pages, 4 figures, 2 ancillary files; updated to refer to newly published results

R2 v1 2026-06-22T15:45:04.626Z