Unformatted text preview: B ′ , by the geometric deFnition of dot product = a 1 b 2 − a 2 b 1 by the formula for B ′ This proves the area interpretation (1) if A and B have the position shown. If their positions are reversed, then the area is the same, but the sign of the determinant is changed, so the formula has to read, ± a 1 a 2 ± area of parallelogram = ±, whichever sign makes the right side ≥. ± b 1 b 2 ± The proof of the analogous volume formula (2) will be made when we study the scalar triple product A ·B ×C . Generalizing (1) and (2), n ×n determinants can be interpreted as the hypervolume in nspace of a ndimensional parallelotope. θ A B A B C θ θ θ θ A B A B b b b 1 2 1 b B B 1...
View
Full Document
 Fall '14
 GuantaoChen
 Geometry, Determinant, Graph Theory, Vector Space, Pallavolo Modena, Parallelepiped

Click to edit the document details