Row Vector

A Row Vector is a vector that is a 1 × m matrix.

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

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/row_vector Retrieved:2015-3-1.
  • In linear algebra, a row vector or row matrix is a 1 × m matrix, i.e. a matrix consisting of a single row of m elements:  : [math]\displaystyle{ \mathbf x = \begin{bmatrix} x_1 & x_2 & \dots & x_m \end{bmatrix}. }[/math] The transpose of a row vector is a column vector: : [math]\displaystyle{ \begin{bmatrix} x_1 \; x_2 \; \dots \; x_m \end{bmatrix}^{\rm T} = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix}. }[/math] The set of all row vectors forms a vector space (row space) which acts like the dual space to the set of all column vectors (see row and column spaces), in the sense that any linear functional on the space of column vectors (i.e. any element of the dual space) can be represented uniquely as a dot product with a specific row vector.

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