Linear Algebra and Its Applications · Problem 6.2.23
Positive Definite Matrices — Gilbert Strang
Mathematics · tests-for-positive-definiteness
Problem
Give a quick reason why each of these statements is true:
(a) Every positive definite matrix is invertible.
(b) The only positive definite projection matrix is P=I.
(c) A diagonal matrix with positive diagonal entries is positive definite.
(d) A symmetric matrix with a positive determinant might not be positive definite!