Linear Algebra 14TBD: The Direct Algebraic Definition of the Determinant

[ulumaika]

I hadn't the slightest clue what my professor was explaining when he went over this, and in 11 minutes you explained it in a way I completely understood. Thank you so much.

[annizheng]

Math is finally beautiful when you explain it. It's clearer than what the textbook explains

[donlansdonlans]

How didnt I know about this before? This is so much simpler than the laplace expansion

[NrSgt]

I dont understand why so many linnear algebra skip this defintion its very simple and rigourous

[kozert]

you have the most beautiful handwriting on a blackboard that i have ever seen, respect for that!

[annali]

this is super Clear and I love your video! the way you speak makes me feel that I can handle this! good luck to everyone in the comment!

[SlingerDomb]

Thank you so so much for making such a nice explanation for this mess. Almost give up until I found this video. THANKS A LOT.

[dmitriidemenev]

That is a great video, yet I believe that you could make it even better. The transition from perceiving a permutation as a tuple to perceiving it as a function could have been made explicit. It is still absolutely amazing, though!

[heinzhuberti]

That is a very good video. Thank you. I like how organized you talk. Your handwriting is also very neat.

[eniomouzinho]

Thanks from Brazil. Nice, amazing video.

[HaykTarkhanyan]

This video is brilliant, thank you very much.

[VeteranVandal]

My man here really cleans his blackboard...

[victortomno]

it is helpful. thank you. I don't if you can to permutations similarity.

[bullpup]

10:26 you only need 3 transpositions, (15)(13)(12) by index notation

[avtarcheema]

thank you so much, sir this is very helpful

[sunilrampuria]

Near the end, I can't understand how you are calculating five swaps. I can see that the given permutation can be expressed as a 4-cycle and a k-cycle is a composite of k-1 transpositions, so the given permutation is a composite of 3 transpositions, this implies that the permutation is odd and hence it's sign is -1.

[CounterTheAnimatorocn]

Nice explanation! I like it very much!

[DrKappaDelta]

For the sign, you could also trace diagonals in the matrix, the ones that go descending from left to right are positive and the ascending ones are negative, like being the inverse of the slope you get if it was a cartesian plane.

[qthequokka]

Hi Professor, based on the theorem that det(A) = det(A-transpose), I'm wondering whether it is also true to express the algebraic definition in such a way that the columns are in order from 1 to N, and the rows are from ɛ(1) to ɛ(N). Would that also work as a definition of the determinant? Thanks!

[kjof]

Great video and great courses. Should the second term on the fourth line of the formula for the 4x4 determinant be a14a21a33a42