Hessian Matrix - Critical Points and Discriminant

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:

    An art whose medium is language will always show a high degree of critical creativeness, for speech is itself a critique of life: it names, it characterizes, it passes judgment, in that it creates.
    Thomas Mann (1875–1955)

    Wonderful “Force of Public Opinion!” We must act and walk in all points as it prescribes; follow the traffic it bids us, realise the sum of money, the degree of “influence” it expects of us, or we shall be lightly esteemed; certain mouthfuls of articulate wind will be blown at us, and this what mortal courage can front?
    Thomas Carlyle (1795–1881)