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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
We compute Num(M) in some cases, mostly with n = 2.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Let L be a degree 2 Galois extension of the field K and M an n × n matrix with coefficients in L.
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Temel Bulgular & Veri:Let⟨ , ⟩ : Ln × Ln → L be the sesquilinear form associated to the involution L → L fixing K .
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Sonuç & Katkı:We compute Num(M) in some cases, mostly with n = 2.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
Let L be a degree 2 Galois extension of the field K and M an n × n matrix with coefficients in L. Let⟨ , ⟩ : Ln × Ln → L be the sesquilinear form associated to the involution L → L fixing K . We use ⟨ , ⟩ to define thenumerical range Num(M) of M (a subset of L), extending the classical case K = R, L = C, and the case of a finitefield introduced by Coons, Jenkins, Knowles, Luke, and Rault. There are big differences with respect to both cases fornumber fields and for all fields in which the image of the norm map L → K is not closed by addition, e.g., c ∈ L maybe an eigenvalue of M , but c ∈/ Num(M). We compute Num(M) in some cases, mostly with n = 2.
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Bu Makaleye Atıf Yap
BALLICO, E. (2022). On the numerical range of square matrices with coefficients in a degree 2 Galois field extension. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 4, 1698–1710. https://ajindex.com/articles/607753