Row vector

Row vector

In linear algebra, a row vector or row matrix is a 1 × "n" matrix, that is, a matrix consisting of a single row: [harvtxt|Meyer|2000, p. 8]

:mathbf x = egin{bmatrix} x_1 & x_2 & dots & x_m end{bmatrix}.

The transpose of a row vector is a column vector::egin{bmatrix} x_1 \ x_2 \ vdots \ x_m end{bmatrix} = egin{bmatrix} x_1 ; x_2 ; dots ; x_m end{bmatrix}^{ m 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 = egin{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} = egin{bmatrix} a_1 & a_2 & a_3end{bmatrix}egin{bmatrix} b_1 \ b_2 \ b_3end{bmatrix}.

Notes

References

*.


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