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A subset M of a Hilbert space H is a linear manifold if it is closed under addition of vectors and scalar multiplication.

A real, nondegenerate n×n symmetric matrix A, and its corresponding symmetric bilinear form Q(v,w)=v^(T)Aw, has signature (p,q) if there is a nondegenerate matrix C such that ...

A pair of quantities (a, b) where ordering is significant, so (a, b) is considered distinct from (b, a) for a!=b.

There are two different definitions of the polar angle. In the plane, the polar angle theta is the counterclockwise angle from the x-axis at which a point in the xy-plane ...

The study of harmonic functions (also called potential functions).

A group of four elements, also called a quadruplet or tetrad.

The distance from the center of a circle to its perimeter, or from the center of a sphere to its surface. The radius is equal to half the diameter.

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.

In an exterior algebra ^ V, a top-dimensional form has degree n where n=dimV. Any form of higher degree must be zero. For example, if V=R^4 then alpha=e_1 ^ e_2 ^ e_3 ^ e_4 ...

A group of three elements, also called a triad. A triple is therefore a 3-tuple.