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Encyclopedia > Row space

In computer science and mathematics, the row space of an m-by-n matrix with real entries is the subspace of Rn 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).


Given a matrix J:

and r1 = (2,4,1,3,2), r2 = (-1,-2,1,0,5), r3 = (1,6,2,2,2), r4 = (3,6,2,5,1)


The row space of J is the subspace of R5 spanned by { r1, r2, r3, r4 }


See also column space, null space.

Topics in mathematics related to linear algebra

Edit (http://en.wikipedia.org/w/wiki.phtml?title=MediaWiki:Space&action=edit)

Vectors | Vector spaces | Linear span | Linear transformation | Linear independence | Linear combination | Basis | Column space | Row space | Dual space | Orthogonality | Eigenvector | Eigenvalue | Least squares regressions | Outer product | Cross product | Dot product | Transpose | Matrix decomposition


  Results from FactBites:
 
Row and column spaces - Wikipedia, the free encyclopedia (280 words)
Hence, a space formed by row vectors or column vectors are said to be a row space or a column space.
Consequently the row space of J is the subspace of R
Since these four row vectors are linearly independent, the row space is 4-dimensional.
quiz7.html (979 words)
A basis for the row space are rows 1, 2, and 3 (taken as column vectors) of the reduced matrix.
The row space of A is simply the nonzero rows of the reduced form of A. Also, since A is 5x7 the dimension of the null space of A must be two (5+2=7).
Notice that the column space of A^{T} is the same as the row space of A. Similarly, the row space of A^{T} is the column sapce of A. The dimension of the column space of A^{T} equals five as there are five vectors in its basis, also, the rank is 5.
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