Hey! Let A be n×n matrix. I am looking for its D eigenvalue- and X eigenvector matrices for which: X×D÷X = A, what's more f(A) = X×f(D)÷X.
In this example:
A = {{1,2},{3,2}}
Let's determine its eigenvectors and -values:
{Da, Xa} = Eigensystem[{{1, 2}, {3, 2}}]
The output: {{4, -1}, {{2, 3}, {-1, 1}}} where the eigenvalues are correct and the eigenvectors are not! Because:
Xa*DiagonalMatrix[Da]/Xa returns {{4, 0}, {0, -1}}
which differs to matrix A. I would like to get {{-1,2/3},{1,1}} as eigenvectors. How to solve the problem?
(I would like to use it for iteration of bigger Carleman matrices. Thank you!)