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In this paper, some algebraic properties of the joint k numerical radius, joint k radius and the joint k norm of matrices are investigated. Moreover, using the joint higher numerical ranges of diagonal matrices which are convex polyhedrons, a description for the shape of the higher numerical ranges of matrix polynomials is given. 2010 Mathematics Subject Classification: 15A60; 15A18; 47A56

Some results on the joint higher numerical ranges and radii of matrices