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A function which satisfies f(tx,ty)=t^nf(x,y) for a fixed n. Means, the Weierstrass elliptic function, and triangle center functions are homogeneous functions. A ...

Given a set of objects S, a binary relation is a subset of the Cartesian product S tensor S.

A covariant tensor of rank 1, more commonly called a one-form (or "bra").

A tensor g whose discriminant satisfies g=g_(11)g_(22)-g_(12)^2>0.

The usual type of vector, which can be viewed as a contravariant tensor ("ket") of tensor rank 1. Contravariant vectors are dual to one-forms ("bras," a.k.a. covariant ...

A module M over a unit ring R is called faithfully flat if the tensor product functor - tensor _RM is exact and faithful. A faithfully flat module is always flat and ...

Let A, B, and C be three polar vectors, and define V_(ijk) = |A_i B_i C_i; A_j B_j C_j; A_k B_k C_k| (1) = det[A B C], (2) where det is the determinant. The V_(ijk) is a ...

The Sherman-Morrison formula is a formula that allows a perturbed matrix to be computed for a change to a given matrix A. If the change can be written in the form u tensor v ...

A semi-Riemannian manifold M=(M,g) is said to be Lorentzian if dim(M)>=2 and if the index I=I_g associated with the metric tensor g satisfies I=1. Alternatively, a smooth ...

The scalar curvature, also called the "curvature scalar" (e.g., Weinberg 1972, p. 135; Misner et al. 1973, p. 222) or "Ricci scalar," is given by R=g^(mukappa)R_(mukappa), ...