Chapter 45: determinant

https://www.bilibili.com/video/BV13e411m7Js

https://www.youtube.com/watch?v=Sv7VseMsOQc

45.1 induction of determinant axioms

45.2 determinant axioms

determinant axioms

{{det(u,v)=det(u+sv,v)det(u,v)=det(u,v+su)translation invariance{det(su,v)=sdet(u,v)det(u,sv)=sdet(u,v)scaling{det(u1+u2,v)=det(u1,v)+det(u2,v)det(u,v1+v2)=det(u,v1)+det(u,v2)decomposition{{det(u,v)=det(u+sv,v)det(u,v)=det(u,v+su)translation invariance{det(u1+su2,v)=det(u1,v)+sdet(u2,v)det(u,v1+sv2)=det(u,v1)+sdet(u,v2)linearity

45.3 determinant theorems or properties

45.4 ellipse area

45.5 Cramer rule geometry perspective