Dergiler / Turkish Journal of Mathematics / 2018 / Cilt: 42 - Sayı: 1

Restriction of a quadratic form over a nite eld to a nondegenerate affine quadric hypersurface

Sayfa
1–11
Yayın Tarihi
2022-11-05
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

This question is related to a question on the numerical range of matrices over a nite eld.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:F q be quadratic forms with h not degenerate.
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Temel Bulgular & Veri:Fix k 2 F q and set C n ( k;h ) F q := f h ( x 1 ;:::;x n ) = k gF n q .
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Sonuç & Katkı:This question is related to a question on the numerical range of matrices over a nite eld.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

Let h;h M : F n q ! F q be quadratic forms with h not degenerate. Fix k 2 F q and set C n ( k;h ) F q := f h ( x 1 ;:::;x n ) = k gF n q . We compute (in many cases) the image of h M j C n ( k;h ) F q . This question is related to a question on the numerical range of matrices over a nite eld.

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Bu Makaleye Atıf Yap

BALLICO, E. (2022). Restriction of a quadratic form over a nite eld to a nondegenerate affine quadric hypersurface. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 1, 1–11. https://ajindex.com/articles/607823

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Kaynakça (6)

  1. Ballico E. The Hermitian null-range of a matrix over a nite eld. arXiv: 1611.08840
  2. Coons JI, Jenkins J, Knowles D, Luke RA, Rault PX. Numerical ranges over nite elds. Linear Algebra Appl 2016; 501: 37-47
  3. Hirschfeld JWP. Projective Geometries over Finite Fields. Oxford, UK: Clarendon Press, 1979
  4. Hirschfeld JWP, Thas JA. General Galois Geometries. Oxford, UK: Oxford University Press, 1991
  5. Ireland K, Rosen M. A Classical Introduction to Modern Number Theory. New York, NY, USA: Springer, 1982
  6. Small C. Arithmetic of Finite Fields. New York, NY, USA: Marcel & Dekker, 1973