In calculus, the second derivative decides whether a critical point of y(x) is a minimum. For functions of multiple variables, the test is whether a matrix of second derivatives is positive definite. In this session we learn several ways of testing for positive definiteness and also how the shape of the graph of ƒ(x) = xT Ax is determined by the entries of A.
Lecture 27: Positive Definite Matrices and Minima
Problem Solving: Positive Definite Matrices and Minima
Work the problems on your own and check your answers when you're done.