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The "perp dot product" a^_|_·b for a and b vectors in the plane is a modification of the two-dimensional dot product in which a is replaced by the perpendicular vector ...

Let ||A|| be the matrix norm associated with the matrix A and |x| be the vector norm associated with a vector x. Let the product Ax be defined, then ||A|| and |x| are said to ...

A bundle or fiber bundle is trivial if it is isomorphic to the cross product of the base space and a fiber.

An action with G=R. Flows are generated by vector fields and vice versa.

Given a Euclidean n-space, H_n=n+1.

Euclidean n-space is denoted R^n.

The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

The upside-down capital delta symbol del , also called "nabla" used to denote the gradient and other vector derivatives. The following table summarizes the names and ...

The upside-down capital delta symbol del , also called "del," used to denote the gradient and other vector derivatives. The following table summarizes the names and notations ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...