Linear Algebra and Its Applications · Problem 3.1.3

Orthogonality — Gilbert Strang

Mathematics · orthogonal-vectors-subspaces

Problem

Two lines in the plane are perpendicular when the product of their slopes is −1-1. Apply this to the vectors x=(x1,x2)x = (x_1,x_2) and y=(y1,y2)y = (y_1,y_2), whose slopes are x2/x1x_2/x_1 and y2/y1y_2/y_1, to derive again the orthogonality condition xTy=0x^Ty = 0.

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