Nonsingular matrix

[Guest]

Hello,

May I know I matrix Z∈CK×K is a Hermitian Positive Definite Matrix, how to prove that matrix Z is a nonsingular matrix?

If Z is a Hermitian Positive Definite Matrix, then it can be decomposed into a strictly lower (T), diagonal (D), and strictly upper (U) triangular part. Does its lower triangular matrix (L=T+D) is also nonsingular matrix? If yes, can you tell me any theorem or books that I can refer to?

Thank you.

Huda