3.4 Row Vector

Types: N/A
Examples: N/A
Constructions: 4.4 Transpose of a Vector
Generalizations: 3.1 Column Vector

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Row Vector

Row vectors are horizontal arrays of numbers. Let $n \in N$ be a positive integer. The vector $\vec{x} \in R^{1 \times n}$ given by

\vec{x} = [\begin{matrix} x_{1} & x_{2} & \dots & x_{n} \end{matrix}]

is a row vector with $n$ entries, $x_{k} \in R$ for $k \in {1, 2, \dots, n}$ , organized in 1 row and $n$ columns.

Remark. When referring to a row vector $\vec{x} \in R^{1 \times n}$ , the superscript on $R$ represents the dimensions $1 \times n$ of the given vector.

$1$ indicates the number of rows.
$n$ indicates the number of columns.
$\times$ separates the number of rows from the number of columns.

Thus, $R^{1 \times n}$ is the set of vectors that have 1 row and $n$ columns.
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Remark. It is less common to refer specifically to row vectors. Thus, you should always write both dimensions when specifically referring to a row vector.
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Thus, R1×n is the set of vectors that have 1 row and n columns. ⧫

Thus, $R^{1 \times n}$ is the set of vectors that have 1 row and $n$ columns.
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