Let $M$ be a real matrix.
According to this, a P-matrix is a square matrix and all of its principal minors are positive.
On the other hand, people use two different definitions to refer to the positive definiteness.
Def 1) $M$ is a positive definite matrix if $x^TMx>0$ for all $x$.
Def 2) $M$ is a symmetric matrix, and it satisfies the condition $x^TMx>0$ for all $x$.
While I try to study the properties of a P-matrix, I found this lecture note(link), and it says, on page 5 line 6, that "A positive definite matrix A ∈ Mn(C) is a hermitian P-matrix."
I guess the author uses the second definition of positive definiteness.
If this is the case, can we say $M$ is a P-matrix if and only if $M$ satisfies the condition $x^TMx>0$ for all $x$?