The following is from WiKi:

In linear algebra, a symmetric n × n real matrix M is said to be positive definite if zTMz is positive, for all non-zero column vectors z of n real numbers; where zT denotes the transpose of z. More generally, an n × n complex matrix M is said to be positive definite if z*Mz is real and positive for all non-zero complex vectors z; where z* denotes the conjugate transpose of z. This property implies that M is an Hermitian matrix.