# Hubbard's & Hubbards "Concrete To Abstract" Function

by CMoore
Tags: concrete to abstract, function, hubbard, hubbards
 P: 16 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
 P: 626 The dot product?
 P: 16 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.
P: 626

## Hubbard's & Hubbards "Concrete To Abstract" Function

Ah good point
 P: 534 I don't see anything special about it; it's just a linear map from Rm to V that takes ei (the ith standard basis vector in Rm) to vi.

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