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An axiom is a proposition regarded as self-evidently true without proof. The word "axiom" is a slightly archaic synonym for postulate. Compare conjecture or hypothesis, both ...

The term "bundle" is an abbreviated form of the full term fiber bundle. Depending on context, it may mean one of the special cases of fiber bundles, such as a vector bundle ...

Each Cartan matrix determines a unique semisimple complex Lie algebra via the Chevalley-Serre, sometimes called simply the "Serre relations." That is, if (A_(ij)) is a k×k ...

A generalization of Grassmann coordinates to m-D algebraic varieties of degree d in P^n, where P^n is an n-dimensional projective space. To define the Chow coordinates, take ...

The divergence theorem, more commonly known especially in older literature as Gauss's theorem (e.g., Arfken 1985) and also known as the Gauss-Ostrogradsky theorem, is a ...

A regular two-dimensional arrangement of squares separated by vertical and horizontal "canals." Looking at the grid produces the illusion of gray spots in the white area ...

Home plate in the game of baseball is an irregular pentagon with two parallel sides, each perpendicular to a base. It seems reasonable to dub such a figure (i.e., a rectangle ...

The term isocline derives from the Greek words for "same slope." For a first-order ordinary differential equation y^'=f(t,y) is, a curve with equation f(t,y)=C for some ...

The Jordan canonical form, also called the classical canonical form, of a special type of block matrix in which each block consists of Jordan blocks with possibly differing ...

A local ring is a ring R that contains a single maximal ideal. In this case, the Jacobson radical equals this maximal ideal. One property of a local ring R is that the subset ...