In linear algebra, a column vector with m {\displaystyle m} elements is an m × 1 {\displaystyle m\times 1} matrix consisting of a single column of m {\displaystyle m} entries. Similarly, a row vector is a 1 × n {\displaystyle 1\times n} matrix, consisting of a single row of n {\displaystyle n} entries. For example, x {\displaystyle {\boldsymbol {x}}} is a column vector and a {\displaystyle {\boldsymbol {a}}} is a row vector:
x = [ x 1 x 2 ⋮ x m ] , a = [ a 1 a 2 … a n ] . {\displaystyle {\boldsymbol {x}}={\begin{bmatrix}x_{1}\\x_{2}\\\vdots \\x_{m}\end{bmatrix}},\quad {\boldsymbol {a}}={\begin{bmatrix}a_{1}&a_{2}&\dots &a_{n}\end{bmatrix}}.}
(Throughout this article, boldface is used for both row and column vectors.) The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector:
[ x 1 x 2 … x m ] T = [ x 1 x 2 ⋮ x m ] , [ x 1 x 2 ⋮ x m ] T = [ x 1 x 2 … x m ] . {\displaystyle {\begin{bmatrix}x_{1}\;x_{2}\;\dots \;x_{m}\end{bmatrix}}^{\rm {T}}={\begin{bmatrix}x_{1}\\x_{2}\\\vdots \\x_{m}\end{bmatrix}},\quad {\begin{bmatrix}x_{1}\\x_{2}\\\vdots \\x_{m}\end{bmatrix}}^{\rm {T}}={\begin{bmatrix}x_{1}\;x_{2}\;\dots \;x_{m}\end{bmatrix}}.}
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