Index rank-$k$ numerical range of matrices

Abstract

We introduce the $\alpha-$higher rank form of the matrix numerical range, which is a special case of the matrix polynomial version of higher rank numerical range. We also, investigate some algebraic and geometrical properties of this set for general and nilpotent matrices. Some examples to confirm the results are brought.

Keywords

• $\alpha-$higher rank numerical range
• index higher rank numerical range
• $\alpha-$numerical range
• index numerical range