- #1

- 65

- 4

Dang this place has a topology and analysis section too, nice.

This is probably a graduate level topic, but I am by no means an expert on these subjects, just things I learn from wikipedia and other people. The commutator is an operation on two linear operators (most often matrices) of the form ##[A,B] = AB - BA.## This is often touted as a measurement of how "badly" two matrices fail to commute, but I don't think it quite is.

I'd like to research what happens when we induce a matrix norm to the commutator, when the matrix norm of the commutator ##|| [A,B] ||^2## actually returns a specific number, I think that's more of a "measurement" of the commutativity of two matrices.

However, why bother? Are there any theoretical or scientific applications for measuring the size of matrix commutators? Possibly in quantum physics, though I don't know that subject in depth, I hope there are more applications than that.

This is probably a graduate level topic, but I am by no means an expert on these subjects, just things I learn from wikipedia and other people. The commutator is an operation on two linear operators (most often matrices) of the form ##[A,B] = AB - BA.## This is often touted as a measurement of how "badly" two matrices fail to commute, but I don't think it quite is.

I'd like to research what happens when we induce a matrix norm to the commutator, when the matrix norm of the commutator ##|| [A,B] ||^2## actually returns a specific number, I think that's more of a "measurement" of the commutativity of two matrices.

However, why bother? Are there any theoretical or scientific applications for measuring the size of matrix commutators? Possibly in quantum physics, though I don't know that subject in depth, I hope there are more applications than that.

Last edited: