Convexity of quadratic functions in two variablesWe return to the example described here. We consider the two quadratic functions , with values The Hessian of is independent of , and given by the constant matrix: We check that the eigenvalues of are positive, since the determinant, as well as the trace, of the above matrix are. Therefore, is convex. Likewise, the Hessian of is This time, the Hessian has a negative eigenvalue, so is not convex.
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