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 Eigenvectors

eigenvalues and eigenvectors of a matrix
 Syntax
 ``` Eigenvectors(M:MAT, X:POLY):LIST ```

 Description
M must be a matrix of numbers, and X an indeterminate.

This function determines the eigenvalues of M, and for each eigenvalue gives a basis of the corresponding eigenspace -- note that the basis is probably not orthogonal. For irrational eigenvalues, the minimal polynomial of the eigenvalue is given (as a polynomial in X), along with the eigenvectors expressed in terms of a root of the minimal polynomial (represented as X).

 Example
 ``` Use R ::= QQ[x]; M := Mat([[1,2,3],[4,5,6],[7,8,9]]); Eigenvectors(M, x); [Record[Eigenspace = [[-1, 2, -1]], MinPoly = x], Record[Eigenspace = [[1, 1/8x + 1/4, 1/4x - 1/2]], MinPoly = x^2 - 15x - 18]] ------------------------------- M := Mat([[0,2,0,0],[1,0,0,0],[0,0,0,2],[0,0,1,0]]); Eigenvectors(M, x); -- two irrational eigenvalues, each with eigenspace of dimension 2 [Record[Eigenspace = [[1, 1/2x, 0, 0], [0, 0, 1, 1/2x]], MinPoly = x^2 - 2]] ------------------------------- ```