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IEVref: | 102-03-04 | ID: | |

Language: | en | Status: Standard | |

Term: | vector, <mathematics> | ||

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Definition: | element of a vector space Note 1 to entry: An Note 2 to entry: A vector in a Euclidean space is characterized by its magnitude and, if it is a non-zero vector, by its direction. Note 3 to entry: A complex vector $U=A+jB$ where and A are real vectors. BNote 4 to entry: A vector is indicated by a letter symbol in sloped boldface type or by an arrow above a sloped lightface letter symbol: with components ${U}_{i}$ can be denoted $({U}_{i})$. UNote 5 to entry: The term "vector" is also used for a vector quantity. Note 6 to entry: In geometry, the term “vector” is often used for a directed line segment in a point space. | ||

Publication date: | 2017-07 | ||

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Replaces: | 102-03-04:2007-08 | ||

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Note 1 to entry: An *n*-dimensional vector is represented by an ordered set of *n* scalars, usually real or complex numbers, which depend on the choice of the base. In matrix notation, these scalars are usually represented as a column matrix:

$U=\left(\begin{array}{c}{U}_{1}\\ {U}_{2}\\ \vdots \\ {U}_{n}\end{array}\right)$

Note 2 to entry: A vector in a Euclidean space is characterized by its magnitude and, if it is a non-zero vector, by its direction.

Note 3 to entry: A complex vector ** U** is defined by a real part and an imaginary part:

$U=A+jB$ where

Note 4 to entry: A vector is indicated by a letter symbol in sloped boldface type or by an arrow above a sloped lightface letter symbol: ** U** or $\overrightarrow{U}$. The vector

Note 5 to entry: The term "vector" is also used for a vector quantity.

Note 6 to entry: In geometry, the term “vector” is often used for a directed line segment in a point space.