Let A be an n × n complex matrix and c = ( c 1 , c 2 , … , c n ) a real n-tuple. The c-numerical range of A is defined as the set W c ( A ) = ∑ j = 1 n c j x j ∗ Ax j : { x 1 , x 2 , … , x n } is an orthonormal basis for C n . When c = ( 1 , 0 , … , 0 ) , W c ( A ) becomes the classical numerical range of A which is often defined as the set W ( A ) = { x ∗ Ax : x ∈ C n , x ∗ x = 1 } . We show that for any n × n complex matrix A and real n-tuple c, there exists a complex matrix B of size at most n ! such that W c ( A ) = W ( B ) . Constructions of the matrix B for some matrices A and real n-tuple c are provided.