Machine Learning, Linear Algebra, Eigenvectors, Eigenvalue, Mathematics.
for all x. A matrix whose all eigenvalues are either positive or 0 is called a positive semi-definite matrix and f(x) ≥ 0 for all x. The definitions of negative definite and negative semi-definite matrices can be followed from 3 & 4. Positive semi-definite matrices guarantee that f(x) = 0 => x = 0.