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Row vector

 

 
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Row vector
 
 
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In linear algebra
Linear algebra

Linear algebra is the branch of mathematics concerned with the study of Euclidean vectors, vector spaces , linear maps , and system of linear equations....
, a row vector or row matrix is a 1 × n matrix
Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, as shown at the right. In addition to a number of elementary, entrywise operations such as matrix addition a key notion is matrix multiplication....
, that is, a matrix consisting of a single row:








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Encyclopedia


In linear algebra
Linear algebra

Linear algebra is the branch of mathematics concerned with the study of Euclidean vectors, vector spaces , linear maps , and system of linear equations....
, a row vector or row matrix is a 1 × n matrix
Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, as shown at the right. In addition to a number of elementary, entrywise operations such as matrix addition a key notion is matrix multiplication....
, that is, a matrix consisting of a single row:

The transpose
Transpose

In linear algebra, the transpose of a matrix A is another matrix AT created by any one of the following equivalent actions:...
 of a row vector is a column vector
Column vector

In linear algebra, a column vector or column matrix is an m × 1 matrix , i.e. a matrix consisting of a single column of elements....
:

The set of all row vectors forms a vector space
Vector space

File:Vector addition ans scaling.pngA vector space is a mathematical structure formed by a collection of vectors: objects that may be Vector addition together and Scalar multiplication by numbers, called scalar s in this context....
 which is the dual space
Dual space

In mathematics, any vector space, V, has a corresponding dual vector space consisting of all linear functionals on V. Dual vector spaces defined on finite-dimensional vector spaces can be used for defining tensors which are studied in tensor algebra....
 to the set of all column vectors.

Notation


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

Operations


  • Matrix multiplication
    Matrix multiplication

    In mathematics, matrix multiplication is the operation of multiplying a matrix with either a scalar or another matrix. This article gives an overview of the various ways to perform matrix multiplication....
     involves the action of multiplying each row vector of one matrix by each column vector of another matrix.


  • The dot product
    Dot product

    In mathematics, the dot product, also known as the scalar product, is an operation which takes two vector over the real numbers R and returns a real-valued scalar quantity....
     of two vectors a and b is equivalent to multiplying the row vector representation of a by the column vector representation of b:


See also

  • Covariance and contravariance of vectors