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column vector : ウィキペディア英語版
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,
:\mathbf = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end \,.
Similarly, a row vector or row matrix is a 1 × ''m'' matrix, that is, a matrix consisting of a single row of ''m'' elements〔, p. 8〕
:\mathbf x = \begin x_1 & x_2 & \dots & x_m \end \,.
Throughout, boldface is used for the row and column vectors. The transpose (indicated by T) of a row vector is a column vector
:\begin x_1 \; x_2 \; \dots \; x_m \end^ = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end \,,
and the transpose of a column vector is a row vector
:\begin x_1 \\ x_2 \\ \vdots \\ x_m \end^ = \begin x_1 \; x_2 \; \dots \; x_m \end \,.
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.
== Notation ==

To simplify writing column vectors in-line with other text, sometimes they are written as row vectors with the transpose operation applied to them.
:\mathbf = \begin x_1 \; x_2 \; \dots \; x_m \end^
or
:\mathbf = \begin x_1, x_2, \dots, x_m \end^
Some authors also use the convention of writing both column vectors and row vectors as rows, but separating row vector elements with commas and column vector elements with semicolons (see alternative notation 2 in the table below).

| align=center| \begin x_1 \\ x_2 \\ \vdots \\ x_m \end \text \begin x_1 \; x_2 \; \dots \; x_m \end^
|-
| Alternative notation 1
(commas, transpose signs)
| align=center| \begin x_1, x_2, \dots, x_m \end
| align=center| \begin x_1, x_2, \dots, x_m \end^
|-
| Alternative notation 2
(commas and semicolons, no transpose signs)
| align=center| \begin x_1, x_2, \dots, x_m \end
| align=center| \begin x_1; x_2; \dots; x_m \end
|}

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Row and column vectors」の詳細全文を読む



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