NUMERICAL RANGE ON COMPLEX n-INNER PRODUCT SPACES

In this note we define n-numerical range of a matrix M 2 Mm(C) with respect to complex n-inner products on Cm(m ¸ n). We show that if n = 1 or n = m, this definition coincides with the classical definition of numerical range. Moreover, we obtain that the n-numerical range of M is equal to the classical numerical range of a similar matrix with M.