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

*.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • row vector — /roh/, Math. a collection of numbers, as the components of a vector, written horizontally. Cf. column vector. [1925 30] * * * …   Universalium

  • row vector — /roh/, Math. a collection of numbers, as the components of a vector, written horizontally. Cf. column vector. [1925 30] …   Useful english dictionary

  • Vector — may refer to: In mathematics * Euclidean vector, a geometric entity endowed with both length and direction, an element of a Euclidean vector space * Coordinate vector, in linear algebra, an explicit representation of an element of any abstract… …   Wikipedia

  • Vector notation — This page is an overview of the common notations used when working with vectors, which may be spatial or more abstract members of vector spaces.The common typographic convention for representing a vector is upright boldface type, as in v for a… …   Wikipedia

  • Row space — In linear algebra, the row space of a matrix is the set of all possible linear combinations of its row vectors. The row space of an m times; n matrix is a subspace of n dimensional Euclidean space. The dimension of the row space is called the… …   Wikipedia

  • Row and column spaces — The row space of an m by n matrix with real entries is the subspace of R n generated by the row vectors of the matrix. Its dimension is equal to the rank of the matrix and is at most min( m , n ).The column space of an m by n matrix with real… …   Wikipedia

  • Vector multidimensional — En programación, un vector multidimensional es un vector que se indexa mediante una lista ordenada de enteros. El número de enteros que se utiliza en esta lista para indexar el vector multidimensional es siempre el mismo y se conoce como la… …   Wikipedia Español

  • Vector-valued function — A vector valued function is a mathematical function that maps real numbers onto vectors. Vector valued functions can be defined as: *mathbf{r}(t)=f(t)mathbfhat{i}+g(t)mathbfhat{j} or *mathbf{r}(t)=f(t)mathbfhat{i}+g(t)mathbfhat{j}+h(t)mathbfhat{k}… …   Wikipedia

  • Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

  • Vector processor — A vector processor, or array processor, is a CPU design where the instruction set includes operations that can perform mathematical operations on multiple data elements simultaneously. This is in contrast to a scalar processor which handles one… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”