1 Catechism Test 1

The Hessian matrix: Eigenvalues, concavity, and curvature

1 Introduction 1 2 The Hessian matrix and the local quadratic approximation2 3 The eigenvalues of the Hessian matrix3 4 Concavity and curvature6 5 Conclusion 7 6 Answers to the exercises8 1 Introduction Students of courses in multivariable calculus are often taught the so-called \D-test" for optimizing functions of two variables: Theorem 1.1.

  Tests, Matrix, Curvature, Eigenvalue, Hessian, The hessian matrix, Concavity, And curvature