Row vector

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In linear algebra, a row vector is a 1 × n matrix, that is, a matrix consisting of a single row:

\mathbf x = \begin{bmatrix} x_1 & x_2 & \dots & x_m \end{bmatrix}.

The transpose of a row vector is a column vector.

The set of all row vectors forms a vector space which is the dual space to the set of all column vectors.

[edit] Notation

Row vectors are sometimes written using the following non-standard notation:

\mathbf x = \begin{bmatrix} x_1, x_2, \dots, x_m \end{bmatrix}.

[edit] Operations

  • Matrix multiplication involves the action of multiplying each row vector of one matrix by each column vector of another matrix.
  • The dot product of two vectors a and b is equivalent to multiplying the row vector representation of a by the column vector representation of b:
\mathbf{a} \cdot \mathbf{b} = \begin{bmatrix} a_1 & a_2 & a_3 \end{bmatrix}\begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix}.