result in linear algebra
C26953
concept
In linear algebra, a result is a proven statement or conclusion—such as a theorem, lemma, or corollary—that follows logically from definitions and previously established facts about vectors, matrices, and linear transformations.
All labels observed (7)
| Label | Occurrences |
|---|---|
| result in linear algebra canonical | 10 |
| determinant | 3 |
| matrix normal form | 3 |
| linear algebra concept | 1 |
| result in normed division algebras | 1 |
| theorem about eigenvalues | 1 |
| theorem in matrix theory | 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: result in linear algebra
Generated description
In linear algebra, a result is a proven statement or conclusion—such as a theorem, lemma, or corollary—that follows logically from definitions and previously established facts about vectors, matrices, and linear transformations.
Instances (19)
| Instance | Via concept surface |
|---|---|
| Cauchy–Schwarz inequality | — |
| Cauchy determinant | — |
| Cauchy interlacing theorem | — |
| Hadamard inequality | — |
| Schmidt orthogonalization | linear algebra concept |
|
Hermite normal form
linked to:
Hermite
|
matrix normal form |
| Hermite normal form | matrix normal form |
| Sylvester determinant | determinant |
| Cayley–Hamilton theorem | — |
| Birkhoff–von Neumann theorem | theorem in matrix theory |
| Jacobian determinant | determinant |
| Jacobi's theorem on determinants | — |
| Hurwitz determinants | determinant |
| Cauchy–Binet formula | — |
| Weyl inequalities | — |
| Courant–Fischer min–max theorem | — |
| Poincaré separation theorem | — |
| Smith normal form | matrix normal form |
| Hurwitz theorem (composition algebras) | result in normed division algebras |