Answer by Carlo for On positive definite matrices and eigenvalues
By definition, a symmetric matrix $A$ is positive-definite whenever all of the eigenvalues of $A$ are positive. On the other hand, if $A$ is not symmetric, then $A$ cannot be positive-definite.Edit: By...
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If I have symmetric matrix $A,$ then why is proving that all of the eigenvalues of $A$ are positive sufficient to show that $A$ is positive definite? Is this also true for non-symmetric matrices?
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