Question: are orthogonal matrices positive definite?
Answer: The space of positive definite orthogonal matrices. The matrix [100−1] is orthogonal and indefinite. [1002] is positive definite and not orthonormal. ... By a positive definite matrix, I mean either a symmetric or asymmetric matrix M∈Rp2 whose quadratic form satisfies ∀x∈Rp∖{0}:xTMx>0.