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The gradient of F is then normal to the hypersurface. Similarly, an affine algebraic hypersurface may be defined by an equation F(x 1, ..., x n) = 0, where F is a polynomial. The gradient of F is zero at a singular point of the hypersurface (this is the definition of a singular point). At a non-singular point, it is a nonzero normal vector.
2 types of mathematical gradients: circular and linear one, both with arrows. The blue arrows direct from white to black. I made it with Inkscape as a replacement for image File:Grad1.jpg
Polski: Przykładowy gradient koloru : liniowy gradient od niebieskiego do czerwonego. Prostopadle do białej linii, kolor wypełnienia prostokąta jest zawsze taka sama, wzdłuż białej linii, niebieski składnikiem zmienia się liniowo od 100% do 0% - dokładnie naprzeciwko czerwonej składowej.
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The curl of the gradient of any continuously twice-differentiable scalar field (i.e., differentiability class) is always the zero vector: =. It can be easily proved by expressing ∇ × ( ∇ φ ) {\displaystyle \nabla \times (\nabla \varphi )} in a Cartesian coordinate system with Schwarz's theorem (also called Clairaut's theorem on equality ...
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A linear, or axial, color gradient. In color science, a color gradient (also known as a color ramp or a color progression) specifies a range of position-dependent colors, usually used to fill a region. In assigning colors to a set of values, a gradient is a continuous colormap, a type of color scheme.
Del is a very convenient mathematical notation for those three operations (gradient, divergence, and curl) that makes many equations easier to write and remember. The del symbol (or nabla) can be formally defined as a vector operator whose components are the corresponding partial derivative operators.