diagonalProperty
P25793
predicate
Indicates a relationship where something possesses or exhibits a diagonal characteristic, alignment, or behavior relative to a reference frame or structure.
All labels observed (4)
| Label | Occurrences |
|---|---|
| diagonalProperty canonical | 4 |
| hasDiagonalEntries | 2 |
| hasMainDiagonal | 2 |
| diagonalizationProperty | 1 |
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: diagonalProperty
Generated description
Indicates a relationship where something possesses or exhibits a diagonal characteristic, alignment, or behavior relative to a reference frame or structure.
Sample triples (9)
| Subject | Object |
|---|---|
| Pascal's triangle | first diagonal consists of all 1s ⓘ |
| Pascal's triangle | second diagonal lists natural numbers n ⓘ |
| Pascal's triangle | third diagonal lists triangular numbers ⓘ |
| Pascal's triangle | fourth diagonal lists tetrahedral numbers ⓘ |
| Jacobi matrix | real sequence via predicate surface "hasMainDiagonal" ⓘ |
| Jacobi matrix | recurrence coefficients a_n via predicate surface "hasDiagonalEntries" ⓘ |
| UpperTriangular | possibly nonzero entries via predicate surface "hasMainDiagonal" ⓘ |
|
Hermitian forms (work on quadratic forms)
surface form:
Hermitian form
|
Hermitian matrix can be unitarily diagonalized via predicate surface "diagonalizationProperty" ⓘ |
| Smith normal form | invariant factors via predicate surface "hasDiagonalEntries" ⓘ |