Hi: Given a fin.dim vector space V over R, and two different bases B_V,B_V' for V , we say that B_V,B'_V are equivalent as bases ( or have the same orientation) , if there exists a matrix T with TB=B', and DetT>0. How do we define equivalent bases for vector spaces over the Complexes.?. If W is a vector space over C, and we are given bases B_W, B'_W , then the matrix L with LB=B' may not have a real-valued determinant. Is there then a way of defining equivalent bases in the second case.? Thanks.