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# Row vector

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

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

The transpose of a row vector is a column vector:

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

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:

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

## 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:

$mathbf\left\{a\right\} cdot mathbf\left\{b\right\} = begin\left\{bmatrix\right\}$
`   a_1  & a_2  & a_3`
end{bmatrix}begin{bmatrix}
`   b_1  b_2  b_3`
end{bmatrix}.

## References

• .

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