Similarly, a row vector or row matrix is a 1 × m matrix, that is, a matrix consisting of a single row of m elements
Throughout, boldface is used for the row and column vectors. The transpose (indicated by T) of a row vector is a column vector
and the transpose of a column vector is a row vector
The set of all row vectors forms a vector space called row space, similarly the set of all column vectors forms a vector space called column space. The dimensions of the row and column spaces equals the number of entries in the row or column vector.
The column space can be viewed as the dual space to the row space, since any linear functional on the space of column vectors can be represented uniquely as an inner product with a specific row vector.