Abstract: Let A be an n×n complex matrix, and let y =(α1,...,αn) be an n-dimensional complex vector. The y-numerical radius of A, denoted by r_y(A), is defined follows: r_y(A) = max {..., x_i = 1,x_i ∈ Cⁿ}, where Cn is an n-dimensional vector space over complex field C. In this paper we study norm properties and stability of y-numerical radius.

Key words: y-numerical radius, seminorm, generalized matrix norm