rank-2 tensor
C2815
concept
A rank-2 tensor is a mathematical object that can be represented as a matrix whose components transform with two indices under a change of basis, generalizing linear maps and bilinear forms in vector spaces.
All labels observed (6)
| Label | Occurrences |
|---|---|
| Piola–Kirchhoff stress tensor | 2 |
| rank-2 tensor canonical | 2 |
| second-order tensor | 2 |
| concept in tensor calculus | 1 |
| energy–momentum tensor | 1 |
| two-point tensor | 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: rank-2 tensor
Generated description
A rank-2 tensor is a mathematical object that can be represented as a matrix whose components transform with two indices under a change of basis, generalizing linear maps and bilinear forms in vector spaces.
Instances (6)
| Instance | Via concept surface |
|---|---|
| Kronecker delta | concept in tensor calculus |
| Cauchy stress tensor | second-order tensor |
| stress–energy tensor | — |
| Einstein tensor | — |
|
Piola–Kirchhoff stress tensors
surface form:
first Piola–Kirchhoff stress tensor
|
Piola–Kirchhoff stress tensor |
| Kirchhoff stress tensor | second-order tensor |