# No positive definite matrix

04/04/2011

It is well known that: Let be a symmetric matrix, if , then is positive definite and all this eigenvalues are positive.

**Now my question is**: if there exists at least a vector , ; and there exists at least a vector , , does has at least one positive eigenvalue and at least one negative eigenvalue?

**The answer is yes**: Proof by contradiction.

No comments yet