Matrix Proof: det(exp A) = exp(Tr A)

[@APaleDot]

7:10
Small correction. You can't order the matrices inside the trace function however you want. You can only rearrange them cyclically. So, for instance, you can do JP⁻¹P or P⁻¹PJ but not JPP⁻¹.

[@slavinojunepri7648]

Can the rearrangement be arbitrary if the matrices involved in the multiplication (which we are taking the trace) have the same dimensions? The cyclical rearrangement is obviously required if the dimensions are different.

[@APaleDot]

@@slavinojunepri7648
No, even if they are all square matrices, they have to be rearranged cyclically (unless they otherwise commute).

[@i.h.i.d9725]

I just started linear algebra this semester, and this video makes me excited about the subject.

[@thomasjefferson6225]

This is a very good video. I really enjoyed it.

[@JohnSmall314]

Very nice and clear explanation

[@csilval18]

Very cool video. Interesting, to the point, well explained...
You should get more views

[@tomkerruish2982]

Alternatively, tr = ln○det○exp.

[@BenfanichAbderrahmane]

det=exp(tr(ln))

[@nabla_mat]

You’re back!

[@soyoltoi]

Very clear and easy to follow

[@jakeaustria5445]

Thank You

[@sirshabiswas3010]

Sir? This could be an insult to you but I was wondering if you could give me a tip on how to find the limits while finding the area using integration. Please don't mind. I really have a hard time figuring out the limits. And lots of love and support! :⁠-⁠)

[@MuPrimeMath]

Sorry, the question is not clear. It's hard for me to give advice on such general topics. I wish you the best of luck.

[@sirshabiswas3010]

@@MuPrimeMath it's okay, no worries. Thanks for your reply. Keep uploading. Lots of love!

[@MyOneFiftiethOfADollar]

Note that we could call this a Simply Beautiful solution, BUT not as beautiful as a Cowboy cheerleader.