Definition, Meaning & Synonyms
nilpotent
Adjective
/ˈnɪlˌpoʊ.tənt/
Definition
Nilpotent refers to a property of an element in algebraic structures, specifically in the context of rings and matrices, where applying an operation multiple times results in a zero element.
Examples
- The matrix A is nilpotent if Ak = 0 for some positive integer k.
- In quantum mechanics, nilpotent operators play a role in certain mathematical formulations.
Meaning
In the context of linear algebra, a nilpotent matrix is one that, when raised to a certain power, becomes the zero matrix.
Synonyms
- Zero matrix
- Nil
