Row space - Definition and Overview

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:

<math>

 J =
 \begin{bmatrix}
   2 & 4 & 1 & 3 & 2\\
   -1 & -2 & 1 & 0 & 5\\
   1 & 6 & 2 & 2 & 2\\
   3 & 6 & 2 & 5 & 1\\
 \end{bmatrix}

<math> 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.