The function is $$f(x; y; z) = 2x^2 + (x + y)^2 + (x + z)^2 + 2ayz.$$ I have seen that it's convex if the associated matrix is semi-definite, but then I don't know how to demonstrate if it's semi-definite. I have tried to find the eigenvalues to see if they are all equal or greater then 0, but I can't find them by hand. Do you have any suggestions? thank you for your time
2026-04-01 05:01:48.1775019708
For which values of a is this quadratic function convex?
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