Column Vector

A Column Vector is a vector that is an m × 1 matrix.

• AKA: Column Matrix.
  • …
• Example(s):
  • a Matrix Column Vector.
  • …
• Counter-Example(s):
  • a Row Vector.
• See: Vector Space, Dual Space, Transpose.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/column_vector Retrieved:2015-3-1.
  • In linear algebra, a column vector or column matrix is an m × 1 matrix, i.e. a matrix consisting of a single column of m elements. : [math]\displaystyle{ \mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix} }[/math] The transpose of a column vector is a row vector and vice versa: : [math]\displaystyle{ \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix}^{\rm T} = \begin{bmatrix} x_1 \; x_2 \; \dots \; x_m \end{bmatrix} }[/math] The set of all column vectors with a given number of elements forms a vector space which is the dual space to the set of all row vectors with that number of elements.

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