An n × n Hermitian matrix M is said to be positive definite (we mark M > 0) if
- x' M x > 0
for all x in Rn.
It is said to be negative definite (we mark M < 0) if
- x' M x < 0
positive semidefinite (we mark M >= 0) if
- x' M x >= 0
and negative semidefinite (we mark M <= 0) if
- x' M x <= 0
Otherwise we say matrix is indefinite (we mark M <> 0).