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A matrix for a round-robin tournament involving n players competing in n(n-1)/2 matches (no ties allowed) having entries a_(ij)={1 if player i defeats player j; -1 if player ...

The interior of the triangle is the set of all points inside a triangle, i.e., the set of all points in the convex hull of the triangle's vertices. The simplest way to ...

A square matrix with nonzero elements only on the diagonal and slots horizontally or vertically adjacent the diagonal (i.e., along the subdiagonal and superdiagonal), [a_(11) ...

(Bailey 1935, p. 25), where _7F_6(a_1,...,a_7;b_1,...,b_6) and _4F_3(a_1,...,a_4;b_1,b_2,b_3) are generalized hypergeometric functions with argument z=1 and Gamma(z) is the ...

The Wronskian of a set of n functions phi_1, phi_2, ... is defined by W(phi_1,...,phi_n)=|phi_1 phi_2 ... phi_n; phi_1^' phi_2^' ... phi_n^'; | | ... |; phi_1^((n-1)) ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, ...

An n×n complex matrix A is called positive definite if R[x^*Ax]>0 (1) for all nonzero complex vectors x in C^n, where x^* denotes the conjugate transpose of the vector x. In ...

Pre-Calculus