1Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
2Department of Mathematics, Shahrood Branch, Islamic Azad University, Shahrood, Iran
Let $n$ and $k$ be two positive integers, $kleq n$ and $A$ be an $n-$square quaternion matrix. In this paper, some results on the $k-$numerical range of $A$ are investigated. Moreover, the notions of $k$-numerical radius, right $k$-spectral radius and $k$-norm of $A$ are introduced, and some of their algebraic properties are studied.