Row vector

Row vector

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In linear algebra, a row vector or row matrix 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:

begin{bmatrix} x_1 x_2 vdots x_m end{bmatrix} = begin{bmatrix} x_1 ; x_2 ; dots ; x_m end{bmatrix}^{rm T}.

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

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}.

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}.

Notes

References

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