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:
“His misfortune was that he loved youth—he was weak to it, it kindled him. If there was one eager eye, one doubting, critical mind, one lively curiosity in a whole lecture-room full of commonplace boys and girls, he was its servant. That ardour could command him. It hadn’t worn out with years, this responsiveness, any more than the magnetic currents wear out; it had nothing to do with Time.”
—Willa Cather (1873–1947)
“Wi’ joy unfeigned brothers and sisters meet,
An’ each for other’s weelfare kindly spiers:
The social hours, swift-winged, unnoticed fleet;
Each tells the uncos that he sees or hears;
The parents, partial, eye their hopeful years;
Anticipation forward points the view:”
—Robert Burns (1759–1796)