mathematical transformation
C3058
concept
A mathematical transformation is a function or operation that systematically maps elements from one set or space to another, often altering their position, scale, orientation, or form while following defined rules.
All labels observed (21)
| Label | Occurrences |
|---|---|
| linear operator | 10 |
| integral transform | 7 |
| mathematical transformation canonical | 6 |
| AES transformation step | 3 |
| mathematical transform | 3 |
| linear map | 2 |
| natural transformation | 2 |
| change of basis | 1 |
| ergodic transformation | 1 |
| fractional linear transformation | 1 |
| geometric operation | 1 |
| iterative transformation | 1 |
| local diagrammatic transformations | 1 |
| mathematical operation | 1 |
| matrix operation | 1 |
| measure-preserving transformation | 1 |
| mixing transformation | 1 |
| modular transformation | 1 |
| orthogonal transform | 1 |
| transform | 1 |
| transformation of elliptic integrals | 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: mathematical transformation
Generated description
A mathematical transformation is a function or operation that systematically maps elements from one set or space to another, often altering their position, scale, orientation, or form while following defined rules.
Instances (43)
| Instance | Via concept surface |
|---|---|
| Kronecker product | matrix operation |
| Arnold cat map | measure-preserving transformation |
| Lefschetz operator | linear operator |
| Laplace transform | integral transform |
| Minkowski sum | geometric operation |
| Weingarten map | linear map |
| MixColumns | AES transformation step |
| AddRoundKey | AES transformation step |
| Gelfand transform | transform |
| MDCT | orthogonal transform |
| Chern character | natural transformation |
| Kramers–Wannier duality in the Ising model | — |
| Hecke operators | linear operator |
| Moyal bracket | mathematical operation |
| Jordan–Wigner transformation | — |
| Bogoliubov transformation | — |
| Lorentz transformation | — |
| dAlembert operator | linear operator |
|
Mellin transform
linked to:
Hjalmar Mellin
|
integral transform |
| Sommerfeld-Watson transform | mathematical transform |
|
Poisson integral
linked to:
Poisson
|
integral transform |
| Poisson integral | integral transform |
| Fourier transform | mathematical transform |
| residual maker matrix | linear operator |
| Landen transformations | iterative transformation |
| Gauss transformation for elliptic integrals | — |
|
Mellin transform
linked to:
Mellin transforms
|
integral transform |
| shape operator | linear operator |
| Reidemeister moves | local diagrammatic transformations |
|
T : z ↦ z + 1
linked to:
T:z ↦ z+1
|
modular transformation |
| SubBytes | AES transformation step |
| Legendre transformation | — |
| Riesz transforms | linear operator |
| Riesz projection | linear operator |
|
Fourier transform
linked to:
Fourier
|
mathematical transform |
| Hilbert transform | integral transform |
| Harish-Chandra projection | linear map |
| Hodge star operator | linear operator |
| Stieltjes transform | integral transform |
|
Möbius transformation
linked to:
Möbius transformations
|
fractional linear transformation |
| Steklov operator | linear operator |
| Bockstein homomorphism | natural transformation |
| Schrödinger operators | linear operator |