Matrices whose field of values is inscribed in a polygon

Matthew J. Fyfe; Yesenia Hernandez; Pietro Paparella; Malini Rajbhandari

Matrices whose field of values is inscribed in a polygon

Rings and Algebras 2023-07-03 v2 Spectral Theory

Authors: Matthew J. Fyfe , Yesenia Hernandez , Pietro Paparella , Malini Rajbhandari

Abstract

In this work, it is shown that if $A$ is an $n$ -by- $n$ convexoid matrix (i.e., its field of values coincides with the convex hull of its eigenvalues), then the field of any $(n-1)$ -by- $(n-1)$ principal submatrix of $A$ is inscribed in the field of $A$ , i.e., the field is tangent to every side of the polygon corresponding to the boundary of the field of $A$ . This result generalizes a special case established by Johnson and Paparella [Amer. Math. Monthly 127 (2020), no. 1,45-53].

Keywords

hadamard matrices

Cite

@article{arxiv.2303.06772,
  title  = {Matrices whose field of values is inscribed in a polygon},
  author = {Matthew J. Fyfe and Yesenia Hernandez and Pietro Paparella and Malini Rajbhandari},
  journal= {arXiv preprint arXiv:2303.06772},
  year   = {2023}
}

Comments

Report for research project undertaken at the 2022 REU Site: Tiling Theory, Knot Theory, Optimization, Matrix Analysis, and Image Reconstruction

Matrices whose field of values is inscribed in a polygon

Abstract

Keywords

Cite

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