Critical Points and Discriminant
If the gradient of f (i.e. its derivative in the vector sense) is zero at some point x, then f has a critical point (or stationary point) at x. The determinant of the Hessian at x is then called the discriminant. If this determinant is zero then x is called a degenerate critical point of f, this is also called a non-Morse critical point of f. Otherwise it is non-degenerate, this is called a Morse critical point of f.
Read more about this topic: Hessian Matrix
Famous quotes containing the words critical and/or points:
“To affect the quality of the day, that is the highest of arts. Every man is tasked to make his life, even in its details, worthy of the contemplation of his most elevated and critical hour.”
—Henry David Thoreau (1817–1862)
“Mankind is not a circle with a single center but an ellipse with two focal points of which facts are one and ideas the other.”
—Victor Hugo (1802–1885)