Re: Orientation? was: Re: [julia-users] different Eigenvalue results Julia vs Matlab

2016-09-10 Thread Tracy Wadleigh
+10**10**10 On Sep 10, 2016 3:32 PM, "Steven G. Johnson" wrote: > > > > On Saturday, September 10, 2016 at 12:20:25 PM UTC-4, Stuart Brorson wrote: >> >> However, from a physics perspective, this bugs me. In physics, an >> important feature of a space is its orientation.

Re: Orientation? was: Re: [julia-users] different Eigenvalue results Julia vs Matlab

2016-09-10 Thread Steven G. Johnson
On Saturday, September 10, 2016 at 12:20:25 PM UTC-4, Stuart Brorson wrote: > > However, from a physics perspective, this bugs me. In physics, an > important feature of a space is its orientation. I should also remind you that a lot of modern physics tries to separate the laws of physics

Re: Orientation? was: Re: [julia-users] different Eigenvalue results Julia vs Matlab

2016-09-10 Thread Christoph Ortner
Yichao is right, you cannot give eigenvectors an orientation; A good way to think of them is as defining linear subspaces. So what is unique is the projector v\|v| \otimes v/|v| or in the case of multiple e-vals the projector onto the eigenspace \sum v_i \otimes v_i. But never the e-evecs

Re: Orientation? was: Re: [julia-users] different Eigenvalue results Julia vs Matlab

2016-09-10 Thread Yichao Yu
On Sat, Sep 10, 2016 at 2:18 PM, Yichao Yu wrote: > > > On Sat, Sep 10, 2016 at 2:12 PM, Stuart Brorson wrote: > >> I don't think you can define that in a continuous way. >>> In general, if your application relies on certain property of the basis, >>> you

Re: Orientation? was: Re: [julia-users] different Eigenvalue results Julia vs Matlab

2016-09-10 Thread Yichao Yu
On Sat, Sep 10, 2016 at 2:12 PM, Stuart Brorson wrote: > I don't think you can define that in a continuous way. >> In general, if your application relies on certain property of the basis, >> you should just normalize it that way. If you don't have a requirement >> than >> you

Re: Orientation? was: Re: [julia-users] different Eigenvalue results Julia vs Matlab

2016-09-10 Thread Stuart Brorson
I don't think you can define that in a continuous way. In general, if your application relies on certain property of the basis, you should just normalize it that way. If you don't have a requirement than you should worry about it. Thanks for the thoughts. I did a little more thinking and

Re: Orientation? was: Re: [julia-users] different Eigenvalue results Julia vs Matlab

2016-09-10 Thread Yichao Yu
On Sat, Sep 10, 2016 at 12:20 PM, Stuart Brorson wrote: > Just a question from a non-mathematician. Also, this is a math > question, not a Julia/Matlab question. > > I agree that Matlab and Julia are both correct -- within the > definitions of eigenvector and eigenvalue they

Orientation? was: Re: [julia-users] different Eigenvalue results Julia vs Matlab

2016-09-10 Thread Stuart Brorson
Just a question from a non-mathematician. Also, this is a math question, not a Julia/Matlab question. I agree that Matlab and Julia are both correct -- within the definitions of eigenvector and eigenvalue they compute, it's OK that one eigenvector differes between the two by a factor -1.