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
