determinants by Leibniz formula and areas

Asked Oct 29 '23 at 04:34

Active Oct 29 '23 at 05:00

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I want to understand what´s the relation between the definition of the determinants by Leibniz and the calculus of areas. I'm not thinking in proofs like the link I will put below. I want to understand what´s the concept that relates the geometric interpretation of determinant and the definition by Leibniz (that set of permutations). It´s like why that formula created by Leibniz means a "thing"(determinant) that represents an area? thanks so much for your help, Alex

Why determinant of a 2 by 2 matrix is the area of a parallelogram?

edited Oct 29 '23 at 05:00

Ricky

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asked Oct 29 '23 at 04:34

Alexandre Russiano Mendes

the first answer in the link you provide doesn't do the trick for you? its the same picture in higher dimensions, just more terms – C Squared Oct 29 '23 at 05:33
no:( it´s a proof. i wanna concept. like start from Leibniz definition and arrive in geometric interpretation. what´s the relation between the permutations of Leibniz definition and area calculus – Alexandre Russiano Mendes Oct 29 '23 at 05:35
that picture is the interpretation. its adding and subtracting volumes of hypercubes to get the volume of the hyperparallelopiped. each of the terms in the sum for the leibniz formula corresponds to the volume of a hypercube needed to compute the volume of the hyperparallelopiped – C Squared Oct 29 '23 at 05:40
the point is that i dont understand why it works. i understood the process – Alexandre Russiano Mendes Oct 29 '23 at 06:09
My video may be helpful to you. – blargoner Oct 29 '23 at 15:24
Thanks so much ☺️ Ur class is Very good – Alexandre Russiano Mendes Oct 30 '23 at 23:38

determinants by Leibniz formula and areas

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