Hubbard's & Hubbards Concrete To Abstract Function

In summary, on page 215 of H&H Vector Calculus, Linear algebra and Differential Forms text, the authors introduce the "concrete to abstract function" as a linear map from R^m to V, which takes the standard basis vector ei to the corresponding vector vi. It is not a scalar product, as the result is a vector, not a number. There does not seem to be a standardized name for this function.
  • #1
CMoore
16
1
Hubbard's & Hubbards "Concrete To Abstract" Function

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
 
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  • #2


The dot product?
 
  • #3


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


Ah good point
 
  • #5


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.
 

Related to Hubbard's & Hubbards Concrete To Abstract Function

1. What is Hubbard's & Hubbards Concrete To Abstract Function?

Hubbard's & Hubbards Concrete To Abstract Function is a psychological theory that explains the cognitive process of how individuals understand abstract concepts by building upon their concrete experiences.

2. How does the Concrete To Abstract Function work?

The Concrete To Abstract Function works by individuals using their previous concrete experiences to create mental representations of abstract concepts. This allows them to better understand and make sense of abstract ideas.

3. What is the importance of the Concrete To Abstract Function?

The Concrete To Abstract Function is important because it helps individuals make connections between their concrete experiences and abstract concepts, leading to a deeper understanding and better retention of information.

4. Can the Concrete To Abstract Function be applied in real-life situations?

Yes, the Concrete To Abstract Function can be applied in various real-life situations, such as in education, problem-solving, and communication. It can also be used in therapy to help individuals process and understand abstract emotions and thoughts.

5. Are there any limitations to the Concrete To Abstract Function?

While the Concrete To Abstract Function is a widely accepted theory, it has been criticized for oversimplifying the cognitive process and neglecting the role of language and culture. Additionally, not all individuals may follow the same sequence of concrete to abstract understanding, as it can vary based on individual experiences and learning styles.

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