I am trying to create the same outputs in Mathematica and Matlab, however I am running into trouble aligning the eigenvectors with the eigenvalues, I think the Matlab is doing something slightly more complex (Ordering/Sorting) than I anticipated.using the example in on the Mathwork website, for [V,D] = eig(A).http://www.mathworks.co.uk/help/matlab/ref/eig.html#btifddh-2TestMatrix = {{1, 2, 3}, {3, 1, 2}, {2, 3, 1}}[V,D] = eig(A)V =-0.5774 + 0.0000i,   0.2887 - 0.5000i,   0.2887 + 0.5000i,  -0.5774 + 0.0000i,  -0.5774 + 0.0000i,  -0.5774 + 0.0000i,  -0.5774 + 0.0000i,   0.2887 + 0.5000i,   0.2887 - 0.5000i,D =   6.0000 + 0.0000i,   0.0000 + 0.0000i,   0.0000 + 0.0000i,   0.0000 + 0.0000i,  -1.5000 + 0.8660i,   0.0000 + 0.0000i,   0.0000 + 0.0000i,   0.0000 + 0.0000i,  -1.5000 - 0.8660i,However running this in Mathematica, I receive the following eigenvectorm = N[Eigensystem[TestMatrix]]DV = DiagonalMatrix[m[[1]]]Vec=N[Eigenvectors[TestMatrix]]Vec={{1., 1., 1.}, {-0.5 - 0.866025 I, -0.5 + 0.866025 I, 1.}, {-0.5 + 0.866025 I, -0.5 - 0.866025 I, 1.}}This is perfectly acceptable, I just now want to get both vectors into the same form.Note The Diagonal Matrix matches, however I seem unable to recreate V.From reading the Matwork example, V is right eigenvectors. In this case the Form [V,D] = eig(A) returns matrix V, whose columns are the right eigenvectors of A such that AV = VD. & The eigenvectors in V are normalized so that the 2-norm of each is 1.Trying to normalise Vec, now in mathematica, I am unable to recreate the results obtained in Matlab. Clearly I am doing something incorrectly, this is where I get a little lost. I have tried the '2-norm' function as described in Matlab, and also the Normalize function, the latter seems a little better but is still incorrect comparing to the results in the matlab example.Could someone explain where I am going wrong with this, or simply how to recreate the same results in mathematica.Here are my (...I assume...) incorrect attempts.Firslty using Normalise.TestMatrix = {{1, 2, 3}, {3, 1, 2}, {2, 3, 1}}vec = N[Eigenvectors[TestMatrix]]Table[Normalize[vec[[i]]], {i, 1, Length[vec]}]{{0.57735, 0.57735, 0.57735}, {-0.288675 - 0.5 I, -0.288675 + 0.5 I,  0.57735 + 0. I}, {-0.288675 + 0.5 I, -0.288675 - 0.5 I,  0.57735 + 0. I}}This quite close, to the Matlab output V, except the matrix seems to have been transposed, times by a negative, and some how the 2nd and 3rd eigenvalues have been switched (Comparing the Egienvalues and Vector columns) Clearly something has gone wrong, I probably shouldn't have used Normalise.However my attempts using Norm(p,2) are nowhere near to the final resul. I see another thread which touches on this topic but doesn't really help.https://stackoverflow.com/questions/5648975/matlab-vs-mathematica-eigenvectorsCan anyone out there explain this?
Comparing Eigenvectors, Mathematica vs. Matlab
linear algebra;matlab;eigensystem;eigenvalues;mathematica