Hermitian octonion matrices and numerical ranges
Leiba Rodman · Electronic Journal of Linear Algebra · 2014
Notions of numerical ranges and joint numerical ranges of octonion matrices are introduced.Various properties of hermitian octonion matrices related to eigenvalues and convex cones, such as the convex cone of positive semidefinite matrices, are described.As an application, convexity of joint numerical ranges of 2 × 2 hermitian matrices is characterized.Another application involves existence of a matrix with a high eigenvalue multiplicity in a given real vector subspace of hermitian matrices.