Recent content by MrJava

Thank you, I think now I need to find my way to understand the explanation from Wiki then :)

Ok I get the point, thank you.

Oops, I meant "Sorry" - - - Updated - - - I am searching around the Internet and I found this on Wiki: Let M be an n × n Hermitian matrix. The following properties are equivalent to M being positive definite: All its eigenvalues are positive. Let P−1DP be an eigendecomposition of M, where P...

Sorry, but It seems straight to me.

My arguments for the problem is as following: A is positive definite matrix with λ is an arbitrary eigenvalue of A x is a non-zero eigenvector corresponding to λ Then: 0<xTAx=xTλx=λ(xTx) and since x'x>0, results λ>0.

When I try to solve the case for XTX I get stuck at the following: xT(XTX)x = xTXTXx = (Xx)TXx Please kindly guide me next step.

Can anyone give me some hints for this question please? Suppose A is positive definite and symmetric. Prove that all the eigenvalues of A are positive. What can you say of these eigenvalues if A is a positive semi definite matrix? Many thanks in advance.