inner product space
C3750
concept
An inner product space is a vector space equipped with an inner product, a function that assigns a scalar to each pair of vectors in a way that generalizes the dot product and induces notions of length and angle.
All labels observed (4)
| Label | Occurrences |
|---|---|
| inner product space canonical | 2 |
| Hilbert space | 1 |
| non-degenerate pairing | 1 |
| rigged Hilbert space | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: inner product space
Generated description
An inner product space is a vector space equipped with an inner product, a function that assigns a scalar to each pair of vectors in a way that generalizes the dot product and induces notions of length and angle.
Instances (5)
| Instance | Via concept surface |
|---|---|
|
Hilbert spaces
surface form:
Hilbert space
|
— |
| Euclidean space | — |
| Weil pairing | non-degenerate pairing |
|
Gelfand triples (rigged Hilbert spaces)
surface form:
Gelfand triple
|
rigged Hilbert space |
| Hardy space | Hilbert space |