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Geometrically, the discriminant of a quadratic form in three variables is the equation of a quadratic projective curve. The discriminant is zero if and only if the curve is decomposed in lines (possibly over an algebraically closed extension of the field). A quadratic form in four variables is the equation of a projective surface.
In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [1] + + =, where the variable x represents an unknown number, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
For a quadratic classifier, the correct solution is assumed to be quadratic in the measurements, so y will be decided based on + + In the special case where each observation consists of two measurements, this means that the surfaces separating the classes will be conic sections (i.e., either a line , a circle or ellipse , a parabola or a ...
A finite-dimensional vector space with a quadratic form is called a quadratic space. The map Q is a homogeneous function of degree 2, which means that it has the property that, for all a in K and v in V : Q ( a v ) = a 2 Q ( v ) . {\displaystyle Q(av)=a^{2}Q(v).}
As an example, in a two dimensional problem, the line that best divides the two groups is perpendicular to . Generally, the data points to be discriminated are projected onto w → {\displaystyle {\vec {w}}} ; then the threshold that best separates the data is chosen from analysis of the one-dimensional distribution.
Repeated discriminants: the discriminant of a quadratic field uniquely identifies it, but this is not true, in general, for higher-degree number fields. For example, there are two non-isomorphic cubic fields of discriminant 3969. They are obtained by adjoining a root of the polynomial x 3 − 21x + 28 or x 3 − 21x − 35, respectively.
Image credits: lowtuned #5. Not worst, but definitely stupidest. My one dog follows me everywhere like Mary's little lamb. One evening I gave the dogs baths and left their jingly collars off while ...
The quadratic programming problem with n variables and m constraints can be formulated as follows. [2] Given: a real-valued, n-dimensional vector c, an n×n-dimensional real symmetric matrix Q, an m×n-dimensional real matrix A, and; an m-dimensional real vector b, the objective of quadratic programming is to find an n-dimensional vector x ...