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According to those pages, matrix measure u(A) is a convex function, and A is a matrix form. So no matter which matrix we put into "u()" function, it always ensures convexity. For instance as you can see on page 26, $$u_1(A)= max_j(a_{jj}+\sum_{i=!j} |a_{ij}|)$$ where a_ij are elements of matrix A. And let^s say that A is Hessian matrix which is derived from very complicated nonconvex nonlinear function.

MY QUESTION is: Although our Hessian matrix's elements are nonlinear and nonconvex, HOW is it POSSIBLE that the measure of Hessian matrix is convex? I can not believe measure of matrix is convex because for previous Hessian matrix, all elements of it which also take place in "u()" function are nonconvex nonlinear and nonconvex. Could you explain this situation to me?