Linear Algebra and Its Applications · Problem 3.3.40

Orthogonality — Gilbert Strang

Mathematics · weighted-inner-product

Problem

W = \begin{bmatrix} 2 & 0 \\ 0 & 1 \end{bmatrix}

, find the

W

-inner product of

x = (2, 3)

and

y = (1, 1)

, and the

W

-length of

x

. What line of vectors is

W

-perpendicular to

y