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* <math>M</math> is positive definite if and only if all of its eigenvalues are positive.
* <math>M</math> is positive semi-definite if and only if all of its eigenvalues are non-negative.
* <math>M</math> is negative definite if and only if all of its eigenvalues are negative.
* <math>M</math> is negative semi-definite if and only if all of its eigenvalues are non-positive.
* <math>M</math> is indefinite if and only if it has both positive and negative eigenvalues.
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