What is a Commutator? - BYJUS What is a Commutator? Commutators are used in DC machines (DC motors and DC generators) universal motors In a motor, a commutator applies an electric current to the windings A steady rotating torque is produced by reversing the current direction in the rotating windings each half turn In a generator, the commutator reverses the current direction with each turn serving as a mechanical
What is a commutator - Mathematics Stack Exchange The second way is to look at the commutator subgroup as a measure of how noncommutative a group is A group is commutative if it has a trivial commutator subgroup (and highly noncommutative if the commutator subgroup is the entire group)
Commutator relationship proof $ [A,B^2] = 2B [A,B]$ You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
The commutator of two matrices - Mathematics Stack Exchange The commutator [X, Y] of two matrices is defined by the equation $$\begin {align} [X, Y] = XY − YX \end {align}$$ Two anti-commuting matrices A and B satisfy $$\begin {align} A^2=I \qu
Center-commutator duality - Mathematics Stack Exchange So here's a sense in which the commutator subgroup and the center are "dual": the commutator is the subgroup generated by all values of $\mathbf {w} (x,y)$, and the center is the subgroup of all elements that don't affect the values of $\mathbf {w} (x,y)$ when you introduce them as factors
Why is the commutator defined differently for groups and rings? The commutator of a group and a commutator of a ring, though similar, are fundamentally different, as you say In each case, however, the commutator measures the "extent" to which two elements fail to commute
Calculating the commutator (derived) subgroup of $S_3$ If $x$ and $y$ are in $S_3$, then their commutator, $x^ {-1}y^ {-1}xy$, is an even permutation So the commutator subgroup is a subgroup of $A_3$, which is just the identity and the 3-cycles