学術雑誌論文

学術雑誌論文

text

Linear Algebra and Its Applications. 2025, 724, p. 62-82

Leaf as a Poincaré convex domain associated with an endomorphism on a real inner product space

Ogawa, Hiroyuki

Elsevier Inc.

英語

text

2025-06-20

https://doi.org/10.1016/j.laa.2025.06.004

Ogawa H., . Leaf as a Poincaré convex domain associated with an endomorphism on a real inner product space. Linear Algebra and Its Applications 724, 62 (2025); https://doi.org/10.1016/j.laa.2025.06.004.

We define a subset of the closure of the upper half plane associated with an endomorphism on a real inner product space, which is called the leaf. When the dimension of the space is at least 3, the leaf is a convex with respect to the Poincaré metric, and contains all eigenvalues with nonnegative imaginary part. Moreover, the leaf of a normal endomorphism is the minimum Poincaré convex domain containing all eigenvalues with nonnegative imaginary part. The most commonly studied convex domain containing eigenvalues is number range. Numerical range is convex with respect to the Euclidean metric on ℂ, so numerical range has less information than leaf about real eigenvalues. We provide a new visual approach to endomorphisms.

This article is licensed under a Creative Commons Attribution 4.0 International License.

102619

Leaf as a Poincaré convex domain associated with an endomorphism on a real inner product space

Ogawa, Hiroyuki

Elsevier Inc.

英語

2025-06-20

Linear Algebra and Its Applications

724

62

82

https://doi.org/10.1016/j.laa.2025.06.004

https://hdl.handle.net/11094/102619