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Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with ...

The Wolfram Physics Project posits the existence of abstract relations between atoms of space whose pattern defines the structure of physical space. In this approach, two ...

The x- (horizontal) coordinate of a point in a two dimensional coordinate system. Physicists and astronomers sometimes use the term to refer to the axis itself instead of the ...

An algorithm that can always be used to decide whether a given polynomial is free of zeros in the closed unit disk (or, using an entire linear transformation, to any other ...

Let f_1(z), ..., f_m(z) for m>=1 be a set of E-functions that (1) form a solution of the system of differential equations y_k^'=q_(k0)+sum_(j=1)^mq_(kj)y_j for q_(kj) in C(z) ...

The Delta-variation is a variation in which the varied path over which an integral is evaluated may end at different times than the correct path, and there may be variation ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) ...

The multicomputational paradigm is a generalization of the computational paradigm to many computational threads of time. In the ordinary computational paradigm, time ...