Quaternionic Numerical Range and Real Subspaces

Abstract

Let W(A) be the numerical range of an n × n quaternionic matrix A and V a real subspace of the skew field of real quaternions. In this note the authors consider the relation among the shape of W(A), the convexity of V∩W(A): and the validity of the equality V∩W(A) = W_v (A), where W_v (A) is the orthogonal projection of W(A) into V.

Keywords:

• Quaternion
• numerical range
• convexity

AMS Subject Classification:

• 15A33
• 15A60

^∗Corresponding author. E-mail: [email protected]

^∗Corresponding author. E-mail: [email protected]

Notes

^∗Corresponding author. E-mail: [email protected]