Re: ANN: Ada 2005 Math Extensions 20120712

["Nasser M. Abbasi" <nma@12000.org>]

On 7/29/2012 9:34 AM, Ada novice wrote:
> On Sunday, July 29, 2012 3:22:46 PM UTC+1, Nasser M. Abbasi wrote:
>>
>> It is the other way around.
>>
>
> Yes I know about eigenvalues and stability in the complex plane. This is why I
>  said that something would have been terribly wrong if Debian lapack and ACML were
>not agreeing on the eigenvalues.
>

Sorry, I misunderstood you. somehow I read what you said as the
eigenvalues were different.

But different eigenvectors magnitudes is not a problem. It is not
uncommon to see this:

-----------------------------
Matlab:
EDU>> A=[1 2;
          3 4]

EDU>> [eigVectors,eigValues]=eig(A)

eigVectors =

    -0.8246   -0.4160
     0.5658   -0.9094


eigValues =

    -0.3723         0
          0    5.3723
-------------------------

Mathematica:

------------------------------
In[5]:= mat={{1,2},
              {3,4}};

eigenVector=Eigenvectors[mat]//N
Out[6]= {{0.457427,1.},{-1.45743,1.}}

eigenVector=Eigenvalues[mat]//N
Out[7]= {5.37228,-0.372281}

-----------------------------

Maple:
-----------------
A:=<<1|2>,<3|4>>:

evalf(LinearAlgebra:-Eigenvectors(A));
                 [ 5.372281324]  [0.4574271076  -1.457427107]
                 [            ], [                          ]
                 [-0.372281324]  [          1.            1.]
-----------------------

You see, eigenvealuses are all the same (as you also said :), but the
eigenvectors have different normalization. Here Maple and Mathematica
used the same. But Matlab was different. (using default call).

--Nasser