The Commutator of Two Matrices

We define the commutator of two matrices which is a special case of the Lie bracket. It is defined by [A,B] = AB-BA, so we see that the commutator vanishes exactly when the matrices commute. We prove several properties of the commutator with the most important being the Jacobi identity.
#mikethemathematician, #mikedabkowski, #profdabkowski

[@jloira01]

Nice. Can you do one about abstract algebra and extensions, fields, Galois Theory?

[@zaphhood4745]

I did not get any of it but still loved it.

[@mikethemathematician]

@zaphhood4745 Thanks for watching!

[@PunisherTR]

One of the most fundamental topic for Quantum Mechanics course. Thx for the video

[@mikethemathematician]

@PunisherTR Thanks! I will add some linear algebra videos on QM too!