Morse Theory
A non-degenerate critical point of a smooth function is a point where the gradient is zero, and the Hessian matrix at that point is invertible. This condition ensures that the critical point is not flat and allows for a clear classification into local minima, maxima, or saddle points, which connects to many important aspects of manifold theory and Morse theory.
congrats on reading the definition of Non-degenerate critical point. now let's actually learn it.