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Hubbard's & Hubbards Concrete To Abstract Function 
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#1
Feb109, 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? Thanks 


#2
Feb109, 10:32 AM

P: 626

The dot product?



#3
Feb109, 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.



#4
Feb109, 10:41 AM

P: 626

Hubbard's & Hubbards Concrete To Abstract Function
Ah good point



#5
Feb109, 05:26 PM

P: 534

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}.



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