Matlab gives different eigenvalue for same matrix

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Suma
Suma 2014-4-26
评论： Suma 2014-4-27
Hello,
why does matlab give me two different eigenvalues for the same matrix? Working for days and found that the source of error is that I get different eigenvalues for same matrix when evaluated in different way and is such that one has even a negative zero(??). I cannot understand the source of error, can anybody help me? below is the code from my work
>> [0.6029;0.0778-0.794*i]
ans =
0.6029
0.0778 - 0.7940i
>> ans*ans'
ans =
0.3635 0.0469 + 0.4787i
0.0469 - 0.4787i 0.6365
>> eig(ans)
ans =
0.0000
1.0000
>> A(:,:,2) =
0.3635 0.0469 + 0.4787i
0.0469 - 0.4787i 0.6365
>> eig(A(:,:,2))
ans =
-0.0000
1.0000
thanks
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Geoff Hayes
Geoff Hayes 2014-4-26
What are you initializing A(:,:,2) with? Are you setting it as
A(:,:,2) = ans*ans';
or
A(:,:,2) = [0.3635 0.0469 + 0.4787i
0.0469 - 0.4787i 0.6365 ];
Because the above two assignments are not strictly the same due to the precision of the doubles written to the console.
For example,
>> ans*ans'
ans =
0.3635 0.0469 + 0.4787i
0.0469 - 0.4787i 0.6365
But if I print out more precision to the doubles then we see that:
>> format long g
>> ans*ans'
ans =
0.36348841 + 0i 0.04690562 + 0.4787026i
0.04690562 - 0.4787026i 0.63648884 + 0i
So I think that is reasonable that you are observing two sets of slighty different eigenvalues (note that your 0.0000 and -0.0000 are both small and nearly identical; the use of format long g would probably show more information) since you are inputs are slightly different (one set more precise than the other).
Suma
Suma 2014-4-26
Hi,
No I am not setting A(:,:,2) = ans*ans';
actually A(:,:,k) for k=1:N are matrices that I get in my program, they in turn are dependent on multiplication of column vectors formed by random variables rand.
after searching for the reason why i get complex number I came to know that A(:,:,k) =A(:,:,2) gives me eigenvalues -0.0000 and 1.0000. I tracked its matrix value and found that it was 0.3635 0.0469 + 0.4787i 0.0469 - 0.4787i 0.6365
So I again recomputed the column vector source that gave me the A(:,:,2) matrix which was 0.6029 0.0778 - 0.7940i
doing multiplication of this matrix as [ 0.6029;0.0778 - 0.7940i]*[ 0.6029;0.0778 - 0.7940i]' or ans*ans' gave me the same matrix(of course), 0.3635 0.0469 + 0.4787i 0.0469 - 0.4787i 0.6365
but now its eigen value are simply 0.0000 1.0000
Having explained this, if the matrix that the program generated (hence matlab) is alright because of precision then I get negative eigenvalue. But this is in contradiction to expected real eigenvalue of the matrix.
On the other hand if the precision is be limited (IDK how), so that I get real eigenvalues(non-negative) then it would make my work easier. But then I would be doing assumption rather than working with real precised mathematical values that matlab is providing.
Of course I want exact results and results are sensitive but don't know how to resolve the above stated problem.
Thanks

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回答（1 个）

Azzi Abdelmalek
Azzi Abdelmalek 2014-4-26
  1 个评论
Suma
Suma 2014-4-27
Hi,
I looked at the wiki but didn't find what I am looking for. For one thing, I did try solving the problem by converting to single precision format but it didn't work.
I want to convert the negative eiqen values to positive.
Thanks

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