# A problem on finding orthogonal basis and projection

by visharad
Tags: basis, orthogonal, projection
 P: 53 Use the inner product = integral f(x) g(x) dx from 0 to 1 for continuous functions on the inerval [0, 1] a) Find an orthogonal basis for span = {x, x^2, x^3} b) Project the function y = 3(x+x^2) onto this basis. --------------------------------------------------------- I know the following: Two vectors are orthogonal if their inner product = 0 A set of vectors is orthogonal if = 0 where v1 and v2 are members of the set and v1 is not equal to v2 If S = {v1, v2, ..., vn} is a basis for inner product space and S is also an orthogonal set, then S is an orthogonal basis. Regarding projection, I know that if W is a finite dimensional subspace of an inner product space V and W has an orthogonal basis S = {v1, v2, ..., vn} and that u is any vector in V then, projection of u onto W = v1/||v1||^2 + v2/||v2||^2 + v3/||v3||^2 + ... vn/||vn||^2 I can calculate integrals, but I really do not know how to fit all these together for this problem. I am not sure how to start.
 P: 53 Please delete this thread. I am posting this problem in Linear and Abstract Algebra forum.

 Related Discussions Calculus & Beyond Homework 2 Calculus & Beyond Homework 2 Calculus & Beyond Homework 1 Linear & Abstract Algebra 8 Linear & Abstract Algebra 1