First question: If A is pd, then A^-1 is pd.
Outline of answer:
If A is pd, then there exists a nonsingular matrix P st A=P'P
Then A^-1 = (P'P)^-1 = (P^-1) * (P^-1)' = (P^-1)' * (P^-1)
3. If (P^-1)' * (P^-1), then there exists a A^-1 that is positive definite
Second question: If...
Thanks for the help! As with many problems...AFTER seeing the answer it seems so simple. This gives me one more technique to approach my homework problems, but unfortunately I'm already stuck on the next one (going to keep working on it for a bit longer before I post the question)
nnd = non negative definite matrix
pd = positive definite I'm having a tough time grappling with the concept of pd, psd matrices in general. My understanding basically just boils down to this, basically after multiplying everything out using the matrix formula x'Ax, you will get some sort of...