compute the eigenvalues and eigenvectors of a matrix
l = eig(A)
[V,L] = eig(A)
[V,L,N] = eig(A)
The function eig(A) computes the eigenvalues and eigenvectors of the matrix A. That is, for each eigenvalue lambda of A, it solves the linear system (I * lambda - A) * X= 0 for X.
When the function is called using the form l := eig(A), the returned value of l is a column Vector containing the eigenvalues of A.
When the function is called using the form V,L := eig(A), the returned value of L is a Matrix with the eigenvalues of A along the main diagonal, and the returned value of V is a Matrix whose columns are the eigenvectors of A.
When the function is called using the form V,L,N := eig(A), L and V are as described above. N is a row vector of indices, one for each linearly independent eigenvector of A, such that the vector corresponding to the ith column of V has eigenvalue L[N[i],N[i]].
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