Register to reply

A problem on finding orthogonal basis and projection

by visharad
Tags: basis, orthogonal, projection
Share this thread:
Nov21-11, 10:23 AM
P: 53
Use the inner product <f,g> = 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 <v1,v2> = 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 = <u, v1> v1/||v1||^2 + <u, v2> v2/||v2||^2 + <u, v3> v3/||v3||^2 + ...<u, vn> 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.
Phys.Org News Partner Mathematics news on
Researcher figures out how sharks manage to act like math geniuses
Math journal puts Rauzy fractcal image on the cover
Heat distributions help researchers to understand curved space

Register to reply

Related Discussions
Orthogonal projection Calculus & Beyond Homework 2
Finding an orthogonal basis? Calculus & Beyond Homework 2
Finding orthogonal basis for the nullspace of a matrix? Calculus & Beyond Homework 1
Orthogonal projection Linear & Abstract Algebra 8
Orthogonal projection, orthonormal basis, coordinate vector of the polynomial? Linear & Abstract Algebra 1