Hubbard's & Hubbards "Concrete To Abstract" Functionby CMoore Tags: concrete to abstract, function, hubbard, hubbards 

#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}.



Register to reply 
Related Discussions  
Difference between "Identical", "Equal", "Equivalent"  Calculus & Beyond Homework  9  
Question about a Theorem in Gallian's "Contemporary Abstract Algebra"  Linear & Abstract Algebra  2  
"Derivative" in an abstract polynomial ring  Calculus & Beyond Homework  1 