Register to reply

Linear Algebra: Orthonormal Basis

by tylerc1991
Tags: algebra, basis, linear, orthonormal
Share this thread:
tylerc1991
#1
Apr14-11, 09:16 PM
P: 166
1. The problem statement, all variables and given/known data

Find an orthonormal basis for the subspace of R^4 that is spanned by the vectors: (1,0,1,0), (1,1,1,0), (1,-1,0,1), (3,4,4,-1)

3. The attempt at a solution

When I try to use the Gram-Schmidt process, I am getting (before normalization): (1,0,1,0), (0,1,0,0), (1,0,-1,2), (0,0,0,0). So obviously there is some mistake that I am making but I have checked this at least 3 times. Can someone help me and let me know if it is something on my end or the problem. Thank you.
Phys.Org News Partner Science news on Phys.org
Mysterious source of ozone-depleting chemical baffles NASA
Water leads to chemical that gunks up biofuels production
How lizards regenerate their tails: Researchers discover genetic 'recipe'
Dick
#2
Apr14-11, 09:29 PM
Sci Advisor
HW Helper
Thanks
P: 25,228
Without have actually worked it out fully, why do you think you made a mistake? The dimension of the subspace is less than 4. You are only going to get a number of orthonormal vectors equal to the dimension of the subspace.
tylerc1991
#3
Apr14-11, 09:33 PM
P: 166
Quote Quote by Dick View Post
Without have actually worked it out fully, why do you think you made a mistake? The dimension of the subspace is less than 4. You are only going to get a number of orthonormal vectors equal to the dimension of the subspace.
I thought that the basis had to span R^4? And since of of the elements was (0,0,0,0) the basis can't span R^4.

Dick
#4
Apr14-11, 09:35 PM
Sci Advisor
HW Helper
Thanks
P: 25,228
Linear Algebra: Orthonormal Basis

Quote Quote by tylerc1991 View Post
I thought that the basis had to span R^4? And since of of the elements was (0,0,0,0) the basis can't span R^4.
It doesn't span R^4. It spans the subspace of R^4 spanned by the given vectors.
tylerc1991
#5
Apr14-11, 09:37 PM
P: 166
Quote Quote by Dick View Post
It doesn't span R^4. It spans the subspace of R^4 spanned by the given vectors.
I see. So will (0,0,0,0) be included in the orthonormal basis?
Dick
#6
Apr14-11, 09:41 PM
Sci Advisor
HW Helper
Thanks
P: 25,228
Quote Quote by tylerc1991 View Post
I see. So will (0,0,0,0) be included in the orthonormal basis?
(0,0,0,0) is in EVERY subspace. You throw that away. It's never part of a basis. A basis is a set of linearly independent vectors. And it certainly isn't normal.


Register to reply

Related Discussions
Algebra : Finding orthonormal basis for the intersection of the subspaces U and V Calculus & Beyond Homework 7
A couple linear algebra questions (basis and linear transformation Calculus & Beyond Homework 5
Linear transformation of an orthonormal basis Calculus & Beyond Homework 1
Another linear algebra problem, basis and linear transformations. Calculus & Beyond Homework 7
Linear Algebra - Linear Transformations, Change of Basis Calculus & Beyond Homework 3