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 Author: WorldMaster [ Thu Jun 21, 2018 4:46 pm ] Post subject: eigenvals problem Hello. I already have a lot of time and can not really figure out how to count eigenvecs in the AlgLib library.Here is an example with a solution in the matkad with which I try to reduce my results:http://old.exponenta.ru/soft/mathcad/learn/la/mathcad/ex3/ex3.htmThere is a matrix:Code: { 1, 2, 3 }, { 0, 1, 2 }, { 3, 4, 1 }Next, I use the alglib.rmatrixevdCode:alglib.rmatrixevd(M, 3, 3, out wr, out wi, out vl, out vr);Here are the results:Code:матрица wrEigenvals-2,710+0,000i0,271+0,000i5,439+0,000iThis corresponds to the eigenvalues ??in the same example of the mitkad, even in an inverted form.But here's the trouble.The library function gives me the result as left and right vectors:Code:EigenvecМатрица vr0.518   -1.000   -0.879   0.539   0.803   -0.451   -1.000   -0.293   -1.000   Матрица vl0.809   -0.708   -0.561   0.642   1.000   -1.000   -1.000   0.172   -0.829In the description they write:Quote:VL, VR - arrays of left and right eigenvectors (if they are needed).If WI[i]=0, the respective eigenvalue is a real number,and it corresponds to the column number I of matrices VL/VR.If WI[i]>0, we have a pair of complex conjugate numbers withpositive and negative imaginary parts:the first eigenvalue WR[i] + sqrt(-1)*WI[i];the second eigenvalue WR[i+1] + sqrt(-1)*WI[i+1];WI[i]>0WI[i+1] = -WI[i] < 0In that case, the eigenvector corresponding to the firsteigenvalue is located in i and i+1 columns of matricesVL/VR (the column number i contains the real part, and thecolumn number i+1 contains the imaginary part), and the vectorcorresponding to the second eigenvalue is a complex conjugate tothe first vector.Arrays whose indexes range within [0..N-1, 0..N-1].How much I did not get into it and did not even try the required result even close.Should be:Code:0,625 0,76 -0,4150,321 -0,611 -0,4320,711 0,222 0,801In general, please poke my nose that where and how do I count to come to the specified result?Thank you.

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