Right eigenvalue equation in quaternionic quantum mechanics

By S. Leo, G. Scolarici. 2000

144 citations recorded by the source corpus.

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n -dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9b6aa846bc35ef7faba9753b46579de02716df0a

Citations in the corpus

• The η-bihermitian solution to a system of real quaternion matrix equations (2014, unknown): “[5–10]).”
• A real quaternion matrix equation with applications (2013, unknown): “, see [1,2,6,10,16,18,20,33].”