Hubbard's & Hubbards "Concrete To Abstract" Function

CMoore

On page 215 of H&H Vector Calculus, Linear algebra and Differential Forms text the authors define something they call the "concrete to abstract function". It is defined as follows:

Let (x_1, ..., x_m) be a point in R^m and let {v_1, ..., v_m} be a set of vectors in V. The, the abstract to concrete function F is given by

F(x_1, ..., x_m) = x_1*v_1 + ... + x_m*v_m.

Is there another name/ standardized name for this function?

Thanks

NoMoreExams

The dot product?

CMoore

No...It's not a scalar product because the result is a vector, not a number; it's a mapping from R^m to V.

NoMoreExams

Ah good point

adriank

I don't see anything special about it; it's just a linear map from R^m to V that takes e_i (the i^th standard basis vector in R^m) to v_i.