High Quality Content by WIKIPEDIA articles! The row space and column space of an m-by-n matrix with real entries is the subspace of Rn generated by the row vectors and column vectors, respectiviely, of the matrix. Its dimension is equal to the rank of the matrix and is at most min(m,n). 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 x n matrix is a subspace of m-dimensional Euclidean space. The dimension of the row space is called the rank of the matrix. The column space of a matrix is the image or range of the corresponding matrix transformation.

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