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## Computing missing Eigenvectors [closed]

Given a $3 \times 3$ real matrix $M$. $M$ has at least one $0$ Eigenvalue and the corresponding Eigenvector is known; I am looking for the other two. Is there an approach to find reduce the matrix $M$ making is possibly non-singular and finding the other two Eigenvectors?

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Notice that after diagonalisation 2x2 matrix A has eigenvalue equation of the shape: f(A,x)) = x^2-tr(A)x+det(A). Similar equations for 3x3 matrix are known: en.wikipedia.org/wiki/… – kakaz Apr 1 2011 at 13:42
@kakaz thanks for the hint. That might bear some potential. – angerman Apr 1 2011 at 19:43
Why can you assume M has a complete set of eigenvectors? – Yemon Choi Apr 1 2011 at 20:59