In particular, R"n" can be interpreted as the space of columns of real numbers, its dual space is typically written as the space of "rows" of real numbers. Such a row acts on R"n" as a linear functional by ordinary matrix multiplication. This is because a functional maps every -vector "x" into a real number "y". Then, seeing this functional as a matrix "M", and "x", "y" as a matrix and a matrix (trivially, a real number) respectively, if then, by dimension reasons, "M" must be a matrix; that is, "M" must be a row vector.