Row and column vectors
Matrix consisting of a single row or column / From Wikipedia, the free encyclopedia
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In linear algebra, a column vector with elements is an matrix[1] consisting of a single column of entries, for example,
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Similarly, a row vector is a matrix for some , consisting of a single row of entries,
(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:
and
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.