چكيده
In this thesis, while introducing the -higher rank numerical range of matrices,
which is a special case of the -higher rank numerical range of matrix polynomials,
some of its algebraic and geometrical properties have been studied. Moreover,
examining the number of connected components, compactness and boundedness of
these sets, the -higher rank numerical range of nilpotent matrices has been studied.
In addition to studying the geometric properties of the conditions that higher rank
numerical range to be connected and in some cases the figure of these sets has been
obtained. Also, the boundearies and sharp points of these sets have been studied and
some relations for the membership of boundary points in the set of sharp points have
been obtained. Examples are provided in each section to make the material clearer.
