Definition For Maps
For a differentiable map f between Rm and Rn, critical points are the points where the differential of f is a linear map of rank less than n; in particular, every point is critical if m < n. This definition immediately extends to maps between smooth manifolds. The image of a critical point under f is a called a critical value. A point in the complement of the set of critical values is called a regular value. Sard's theorem states that the set of critical values of a smooth map has measure zero.
Read more about this topic: Critical Point (mathematics)
Famous quotes containing the words definition and/or maps:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“And at least you know
That maps are of time, not place, so far as the army
Happens to be concerned—the reason being,
Is one which need not delay us.”
—Henry Reed (1914–1986)