Positive definite matrices and positive semi-definite matrices.
Some authors do not require positive definite matrices to be a subclass of Hermitian matrices. This means a real matrix remains to be positive definite up to addition by an arbitary antisymmetric matrix, but then its eigenvalues can have nonzero imaginary parts (and positive real parts).
Thm: 7.2.5; Thm: 7.2.6; Cor: 7.2.7;