Affine construction of signed measures via the determinant (part 1) | Abstract Algebra 10

More in my "untying knots in linear algebra"/"wtf is the determinant" mini-series.This is an interpretation of determinants that was new to me until recently. And it's quite elegant.

Note: when I was saying "angle" during the middle of the video, I meant "spread". We can measure the size of a line segment (quadrance) and the separation between two lines (spread). See Wildberger's rational trigonometry (linked below) for more details.

WildTrig playlist: https://www.youtube.com/playlist?list=PL3C58498718451C47
Divine Proportions book (Wildberger's book on rational trigonometry): https://www.wildegg.com/store/p4/product-divine-proportions-hardback-book.html