An n×nn\times nn×n Hermitian complex matrix MMM is positive definite if ⟨x,Mx⟩>0\langle x, Mx\rangle > 0⟨x,Mx⟩>0 for all x≠0x\neq 0x=0 in Cn\mathbb C^nCn where ⟨⋅,⋅⟩\langle\cdot,\cdot\rangle⟨⋅,⋅⟩ is the standard inner product on Cn\mathbb C^nCn
If we allow the dot product to be zero, then MMM is postive semidefinite.
Wikidata ID: Q1052034