Details

Autor(en) / Beteiligte

• Chien, Mao-Ting
• Nakazato, Hiroshi

Titel

Inverse numerical range and Abel-Jacobi map of Hermitian determinantal representation

Ist Teil von

• Linear algebra and its applications, 2022-01, Vol.633, p.227-243

Ort / Verlag

Amsterdam: Elsevier Inc

Erscheinungsjahr

2022

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Let A be an n×n matrix. The Hermitian parts of A are denoted by ℜ(A)=(A+A⁎)/2 and ℑ(A)=(A−A⁎)/(2i). The kernel vectors of the linear pencil xℜ(A)+yℑ(A)+zIn play a role for the inverse numerical range of A. This kernel vector technique was applied to perform the inverse numerical range of 3×3 symmetric matrices. In this paper, we follow the kernel vector method and apply the Abel theorem for 3×3 Hermitian matrices. We present the elliptic curve group structure of the cubic curve associated to the ternary form of the matrix, and characterize the Abel type additive structure of the divisors of the cubic curve. A numerical example is given to illustrate the characterization related to the Riemann theta representation.