Kunze Linear Algebra · Problem 8.2.7

Inner Product Spaces

Mathematics — Methods · orthogonal-projection

Problem

Let

V

be the inner product space consisting of

R^2

and the inner product whose quadratic form is defined by

\|(x_1, x_2)\|^2 = (x_1 - x_2)^2 + 3x_2^2.

Let

E

be the orthogonal projection of

V

onto the subspace

W

spanned by the vector

(3, 4)

. Now answer the four questions of Exercise 6.