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Hubbard's & Hubbards Concrete To Abstract Function

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Feb1-09, 08:41 AM
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?

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Feb1-09, 10:32 AM
P: 626
The dot product?
Feb1-09, 10:38 AM
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.

Feb1-09, 10:41 AM
P: 626
Hubbard's & Hubbards Concrete To Abstract Function

Ah good point
Feb1-09, 05:26 PM
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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