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# Vectors

A vector is a linear array of numbers, symbols, or expressions, arranged either in rows (row vectors) or columns (column vectors). (A vector is a tensor of rank 1.) The individual items in a vector are called its elements or entries.

## Contents

An ${\displaystyle n}$ vector ${\displaystyle \mathbf {V} }$ is commonly written using box brackets (an alternative notation uses large parentheses instead). An ${\displaystyle n}$ column vector ${\displaystyle \mathbf {V} }$ is written

${\displaystyle \mathbf {V} ={\begin{bmatrix}{\begin{array}{cccccc}v_{1}\\v_{2}\\\vdots \\v_{n}\end{array}}\end{bmatrix}}=\left({\begin{matrix}{\begin{array}{cccccc}v_{1}\\v_{2}\\\vdots \\v_{n}\end{array}}\end{matrix}}\right),}$

while an ${\displaystyle n}$ row vector ${\displaystyle \mathbf {W} }$ is written

${\displaystyle \mathbf {W} =\mathbf {V} ^{\rm {T}}={\begin{bmatrix}{\begin{array}{cccccc}v_{1}&v_{2}&\cdots &v_{n}\end{array}}\end{bmatrix}}=\left({\begin{matrix}{\begin{array}{cccccc}v_{1}&v_{2}&\cdots &v_{n}\end{array}}\end{matrix}}\right),}$

where ${\displaystyle \mathbf {V} ^{\rm {T}}}$ is the transpose of ${\displaystyle \mathbf {V} }$.

An example of a column vector with 5 entries is

${\displaystyle {\begin{bmatrix}{\begin{array}{rrrrr}9\\-5\\7\\1\\19\end{array}}\end{bmatrix}},}$

while an example of a row vector with 5 entries is

${\displaystyle {\begin{bmatrix}{\begin{array}{rrrrr}9&-5&7&1&19\end{array}}\end{bmatrix}}.}$