Row and column vectors

In linear algebra, a column vector or column matrix is an m × 1 matrix, that is, a matrix consisting of a single column of m elements,

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.

This page was last edited on 14 November 2017, at 12:20.
Reference: https://en.wikipedia.org/wiki/Column_vector under CC BY-SA license.

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