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The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated ...
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), canonical variates analysis (CVA), 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 ...
Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.
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 , the following ratio:
In mathematics, the conductor-discriminant formula or Führerdiskriminantenproduktformel, introduced by Hasse (1926, 1930) for abelian extensions and by Artin () for ...
It is possible to calculate the extent to which the two scales overlap by using the following formula where is correlation between x and y, is the reliability of x, and is the reliability of y: r x y r x x ⋅ r y y {\displaystyle {\cfrac {r_{xy}}{\sqrt {r_{xx}\cdot r_{yy}}}}}