If `x` is an eigenvector, then `-x` is also an eigenvector (and with the
same norm).
On Monday, November 23, 2015 at 3:58:31 AM UTC+1, Michael Bullman wrote:
>
> Hi All,
>
> I have a pretty easy question about how/why the svd() behaves how it does.
>
> Why are my U and V matrices always a factor of -1 from the textbook
> examples? I'm just getting my feet wet with all this, so I wanted to check
> what the function returns vs what the textbook says the answers would be,
> and it looks like it's always off by negative one.
>
> julia> A = [1 2 ; 2 2; 2 1]
> 3x2 Array{Int64,2}:
> 1 2
> 2 2
> 2 1
>
> julia> U, s, V = svd(A, thin=false)
> (
> 3x3 Array{Float64,2}:
> -0.514496 0.707107 0.485071
> -0.685994 0.0 -0.727607
> -0.514496 -0.707107 0.485071,
>
> [4.123105625617661,0.9999999999999999],
> 2x2 Array{Float64,2}:
> -0.707107 -0.707107
> -0.707107 0.707107)
>
>
> text book shows the 1,1 entry of U to be
> julia> 3/sqrt(34)
> 0.5144957554275265
>
> without a negtive sign. really just all the negative signs are reversed.
> source: http://www.math.iit.edu/~fass/477577_Chapter_2.pdf
>
> 2nd example:
> julia> A = [3 2 -2 ; 2 3 -2]
> 2x3 Array{Int64,2}:
> 3 2 -2
> 2 3 -2
>
> julia> U, s, V = svd(A, thin=false)
> (
> 2x2 Array{Float64,2}:
> -0.707107 -0.707107
> -0.707107 0.707107,
>
> [5.744562646538029,1.0],
> 3x3 Array{Float64,2}:
> -0.615457 -0.707107 0.348155
> -0.615457 0.707107 0.348155
> 0.492366 5.55112e-17 0.870388)
>
> which is U and V are negative
> http://www.d.umn.edu/~mhampton/m4326svd_example.pdf
>
> So did I just get back luck with example problems? I feel like it's
> probably just a difference in convention or something, but figured I would
> ask for a definitive answer. Thank you for any help
>
>
