八元数本征值问题

八元Mobius变换

Octonionic Mobius Transformations

一个令人烦恼的问题，涉及非结合性解决，允许一般的复杂的莫比乌斯变换的八元数。这是通过将八元莫比乌斯变换与10维时空中的洛伦兹群相关联来实现的。研究10维中类光物体的物理学家们将对这一结果特别感兴趣。

八元数结构算子及其右谱

Octonionic structure operator and its right spectrum

研究仅用八元数乘法定义的规范$G_2$-等变算子$h$的实谱和八元数右特征值问题，通过$G_2$分解和$\mathrm{SU}(3)$块分解得到谱轨迹。

Octonions, E6, and Particle Physics

In 1934, Jordan et al. gave a necessary algebraic condition, the Jordan identity, for a sensible theory of quantum mechanics. All but one of the algebras that satisfy this condition can be described by Hermitian matrices over the complexes or quaternions. The remaining, exceptional Jordan algebra can be described by 3x3 Hermitian matrices over the octonions. We first review properties of the octonions and the exceptional Jordan algebra, including our previous work on the octonionic Jordan eigenvalue problem. We then examine a particular real, noncompact form of the Lie group E6, which preserve…

Constructive methods for spectra with three nonzero elements in the nonnegative inverse eigenvalue problem

We present and compare three constructive methods for realizing non-real spectra with three nonzero elements in the nonnegative inverse eigenvalue problem. We also provide some necessary conditions for realizability and numerical examples. In particular, we utilise the companion matrix.

Eigenvalue problem for some special class of anti-triangular matrices

We study the eigenvalue problem for some special class of anti-triangular matrices. Though the eigenvalue problem is quite classical, as far as we know, almost nothing is known about properties of eigenvalues for anti-triangular matrices. In this paper, we show that there is a nice class of anti-triangular matrices whose eigenvalues are given explicitly by their elements. Moreover, this class contains several interesting subclasses which we characterize in terms of probability measures. We also discuss the application of our main theorem to the study of interacting particle systems, which are …