linearity
P58258
predicate
Indicates that a relationship between quantities preserves addition and scalar multiplication, so outputs change in direct proportion to inputs.
All labels observed (1)
| Label | Occurrences |
|---|---|
| linearity canonical | 10 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: linearity
Generated description
Indicates that a relationship between quantities preserves addition and scalar multiplication, so outputs change in direct proportion to inputs.
Sample triples (10)
| Subject | Object |
|---|---|
| Kronecker product | bilinear in both arguments ⓘ |
| Laplace transform | L{a f(t) + b g(t)} = a L{f(t)} + b L{g(t)} ⓘ |
| Laplace equation | linear ⓘ |
| Laplace operator | linear ⓘ |
| Dirac delta function | linear functional ⓘ |
| Hadamard product (of power series) | bilinear over the base field ⓘ |
| Dirichlet convolution | linear in each argument over pointwise addition of functions ⓘ |
| dAlembert operator | linear ⓘ |
| Hodge Laplacian | linear operator ⓘ |
| Bochner integral | is linear in the integrand ⓘ |