nilpotent background

nilpotent

/ˈnɪlpəˌtɛnt/ /ˈnaɪlpoʊˌtɛnt/

Illustration nilpotent - Image 1

noun

幂零元

A nilpotent element.

Examples :

"In this ring of matrices, the matrix A is a nilpotent, since A squared equals the zero matrix. "

在这个矩阵环中，矩阵A是一个幂零元，因为A的平方等于零矩阵。

Illustration nilpotent - Image 1

adjective

幂零的，零势的

(of an element x of a semigroup or ring) Such that, for some positive integer n, xn = 0.

Examples :

"In this special type of algebra, the matrix "A" is nilpotent because when multiplied by itself three times (A³), the result is the zero matrix. "

在这种特殊的代数中，矩阵“A”是幂零的/零势的，因为当它自己乘以自己三次 (A³) 时，结果是零矩阵。