
#1
Aug2711, 08:00 AM

P: 150

Why is an orthogonal basis important?




#2
Aug2711, 08:36 AM

Mentor
P: 16,545

They're important in so many ways. For example, in Fourier series, where we can say
[tex]x=\sum_{i=1}^n{\frac{<x,e_i>}{<e_i,e_i>}e_i}[/tex] And this provides the very foundation for trigonometric series and harmonic analysis. 



#3
Aug2711, 09:05 AM

P: 100

Because basis vectors have got to be orthogonal ( perpendicular ) so that they are Linearly Independent and one of them can not be formed from any combo of others.
Take i , j , k can you solve for a ,b ,c in ai+bj+ck = 0 without setting all to zero ? 



#4
Aug2711, 10:28 AM

C. Spirit
Sci Advisor
Thanks
P: 4,921

Orthogonal basis 



#5
Aug2711, 01:32 PM

P: 100





#6
Aug2711, 03:21 PM

P: 5,462

Any set of enough non parallel vectors from a vector space can be used as a basis. However finding the correct coefficients is more difficult (laborious) than for an orthogonal set since the orthogonality means they can be found one at a time. 


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