basis in functional analysis
C38660
concept
A basis in functional analysis is a (typically countable) collection of vectors in a topological vector space such that every element of the space can be uniquely represented as a convergent linear combination of these vectors.
All labels observed (3)
| Label | Occurrences |
|---|---|
| basis in functional analysis canonical | 2 |
| basis set in quantum chemistry | 1 |
| family of orthogonal functions | 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: basis in functional analysis
Generated description
A basis in functional analysis is a (typically countable) collection of vectors in a topological vector space such that every element of the space can be uniquely represented as a convergent linear combination of these vectors.
Instances (4)
| Instance | Via concept surface |
|---|---|
| Schauder basis | — |
| Hermite functions | family of orthogonal functions |
|
Slater-type orbital basis sets
surface form:
Slater-type orbital basis set
|
basis set in quantum chemistry |
| Riesz basis | — |