I'm trying to show that the following matrix:
is positive definite. Using the typical definitions I get to this inequality:
x^2 + 2x*(2y+3z) + 5y^2 + 2*y*z + 36z^2 > 0. I just don't know to show that this is true.
Also, I'm trying to show that this matrix:
is NOT positive definite. I can't find a vector x that shows x^T*B*x > 0.
Thanks a lot for your help.