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A complete metric space is a metric space in which every Cauchy sequence is convergent. Examples include the real numbers with the usual metric, the complex numbers, ...

Vector subtraction is the process of taking a vector difference, and is the inverse operation to vector addition.

A vector difference is the result of subtracting one vector from another. A vector difference is denoted using the normal minus sign, i.e., the vector difference of vectors A ...

Given a principal bundle pi:A->M, with fiber a Lie group G and base manifold M, and a group representation of G, say phi:G×V->V, then the associated vector bundle is ...

A vector whose elements are complex numbers.

The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler ...

A vector whose elements are real numbers.

For a curve with radius vector r(t), the unit tangent vector T^^(t) is defined by T^^(t) = (r^.)/(|r^.|) (1) = (r^.)/(s^.) (2) = (dr)/(ds), (3) where t is a parameterization ...

The normalized vector of X is a vector in the same direction but with norm (length) 1. It is denoted X^^ and given by X^^=(X)/(|X|), where |X| is the norm of X. It is also ...

A vector sum is the result of adding two or more vectors together via vector addition. It is denoted using the normal plus sign, i.e., the vector sum of vectors A, B, and C ...