# how to find thet a given real symmetric matrix is positive definite, positive semidefinite, negative definite, negative semidefinite or indefinite.

How to find that a given real symmetric matrix is positive definite, positive semidefinite, negative definite, negative semidefinite or indefinite.; on the basis of principle diagonal minor.

A real symmetric matrix $A$, is positive semidefinite iff all the principal minors of $A$ are nonnegative.