Linear Algebra 14TBD: The Transpose Property of the Determinant

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I can only recommend watching to the end, even if you think you understand before - the close observation of the sign is very insightful!
Everyone who studied permutations in the context of abstract algebra will enjoy the simple rearrangements presented here.

TheLeontheking

This is amazing, thank you so much for revealing the beauty of the mathematics. why not upload videos for Calc I. I am looking forward to your precious videos

cardinalblues

the segment crossing argument nicely worked out Aitken's Determinants and Matrices
that flopping the diagram upside down maintains the number of crossings can be seen as correct by a middle schooler

dacianbonta

I've really been enjoying this series up until now, but I guess I don't really have the proper permutation background here. The only thing I ever really learned about permutations was the formula used for things like 5 choose 3. Where would you recommend I go to brush up on this stuff?

MFMegaZeroX

if you base the permutations with respect to, say, 23451 for the 5x5 case will the determinant still be equivalent to one where the base permutation was 12345, as shown in the video? i understand the signs will be different, but my intuition wants to say that the cumulative effect from the transpositions will either produce a determinant with the same value or an inversed value between cases.

dereksmetzer

Aij is permutate j to i, Aji is permutate i to j, so they are inverse permutation.

marxman

I just can not see it :( I try to see other proofs for this property, but they all use other properties (|AB|=|A||B|, Affect of row operations on determinants etc'...). There is NOTHING in this algebraic formula which somehow shows me that |A|=|At| FOR THE GENERAL CASE. Easy to see for 3X3, O.K, but we can not do it further, 4X4 and so on . . .I guess IM HOPELESS in the case of determinants

atnn

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