In linear algebra, a column vector with ${\displaystyle m}$ elements is an ${\displaystyle m\times 1}$ matrix consisting of a single column of ${\displaystyle m}$ entries, for example,

Similarly, a row vector is a ${\displaystyle 1\times n}$ matrix for some ${\displaystyle n}$, consisting of a single row of ${\displaystyle n}$ entries,

The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector:

The set of all row vectors with n entries in a given field (such as the real numbers) forms an n-dimensional vector space; similarly, the set of all column vectors with m entries forms an m-dimensional vector space.

The space of row vectors with n entries can be regarded as the dual space of the space of column vectors with n entries, since any linear functional on the space of column vectors can be represented as the left-multiplication of a unique row vector.