422 CHAPTER 10 complicated. Moreover, it is worth noting that the functions defin- ing it are not all convex, but that the set of all positive semidefinite matrices is convex. Example 10.2.6 Give the minor criteria for positive semidefinite- ness of symmetric 2 × 2 matrices A and show that not all functions defining this system are convex. Solution. A symmetric 2 × 2 matrix A is positive semidefinite if and only if a 11 0, a 22 0, a 11 a 22 - a 2 0. 12 The function a 11 a 22 - a 2 is not convex, as the quadratic function of 12 one variable a 12 -a 2 is not convex. 12 Conclusion to section 10.2. We have established the concept of ordering vectors by means of a convex cone.