commutator background

commutator

/ˈkɑmjəteɪtər/ /ˈkɑməteɪtər/

Illustration commutator - Image 1

Illustration commutator - Image 2

noun

换向器, 整流器

An electrical switch, in a generator or motor, that periodically reverses the direction of an electric current.

Examples :

"The small motor in my son's toy car has a commutator that flips the current, allowing the wheels to keep spinning in the same direction. "

我儿子玩具车上的小马达里有一个换向器，它能反转电流的方向，使轮子可以一直朝同一个方向转动。

electronics device machine electric technology

Illustration commutator - Image 1

noun

交换子，换位子

A binary map in a given group G, given by [g, h] = ghg−1h−1, where g and h are elements of G, which yields the group's identity if and only if the group operation commutes for g and h.

Examples :

"In group theory, the commutator of two elements tells us how much those elements fail to commute; if the commutator equals the identity element, then the elements commute perfectly. "

在群论中，两个元素的交换子/换位子衡量了这两个元素在多大程度上不能交换顺序；如果交换子/换位子等于单位元，那么这两个元素就可以完全交换顺序。

math group logic

Illustration commutator - Image 1

noun

交换子

A binary map in a given ring R, given by [a, b] = ab − ba, where a and b are elements of R, which yields the ring's zero element if and only if the multiplication operation commutes for a and b.

Examples :

"In abstract algebra, the commutator [x, y] = xy - yx shows us how much two elements x and y fail to commute; if the commutator equals zero, then x and y commute perfectly. "

在抽象代数中，交换子 [x, y] = xy - yx 告诉我们元素 x 和 y 在乘法运算中无法交换的程度；如果交换子等于零，那么 x 和 y 的乘法运算是完全可交换的。

math logic technical science system