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In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number theory, and algebraic ...
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events.
In mathematics, the symbolic method in invariant theory is an algorithm developed by Arthur Cayley, [1] ... Example: the discriminant of a binary quadratic form
The simplest examples of resolvents are X 2 − Δ {\displaystyle X^{2}-\Delta } where Δ {\displaystyle \Delta } is the discriminant , which is a resolvent for the alternating group . In the case of a cubic equation , this resolvent is sometimes called the quadratic resolvent ; its roots appear explicitly in the formulas for the roots of a ...
The discriminant of K is 49 = 7 2. Accordingly, the volume of the fundamental domain is 7 and K is only ramified at 7. In mathematics, the discriminant of an algebraic number field is a numerical invariant that, loosely speaking, measures the size of the (ring of integers of the) algebraic number field.
The method of reduction of order is used to obtain a second linearly independent solution to this differential equation using our one known solution. To find a second solution we take as a guess y 2 ( x ) = v ( x ) y 1 ( x ) {\displaystyle y_{2}(x)=v(x)y_{1}(x)} where v ( x ) {\displaystyle v(x)} is an unknown function to be determined.
where is the number of examples of class . The goal of linear discriminant analysis is to give a large separation of the class means while also keeping the in-class variance small. [ 4 ] This is formulated as maximizing, with respect to w {\displaystyle \mathbf {w} } , the following ratio:
It has the smallest discriminant of all totally real cubic fields, namely 49. [4] The field obtained by adjoining to Q a root of x 3 + x 2 − 3x − 1 is an example of a totally real cubic field that is not cyclic. Its discriminant is 148, the smallest discriminant of a non-cyclic totally real cubic field. [5]