the stability of ODE by studying the eigenvalues

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I'm trying to study the stability of systems of odes but i fail to find the steps of positive and zero eigenvalues; and in the case of negative and zero eigenvalues.

What is the procedure to follow if one of the eigenvalues is equal to zero and the rest are of a positive signs?

What is the procedure to follow if one of the eigenvalues is equal to zero and the rest are negative signs?