有实数元素的m × n 矩阵的行空间是R的由这个矩阵的行矢量生成的子空间。它的维度等于矩阵的秩，最大为min(m,n)。

有实数元素的m × n 矩阵的列空间是R的由这个矩阵的列矢量生成的子空间。它的维度等于矩阵的秩，最大为min(m,n)。

如果把矩阵当作从R到R的线性变换，则矩阵的列空间等于这个线性变换的像。

矩阵A的列矢量是所有A的纵列的线性组合。如果A = [a₁, ...., a_n]，则Col A = Span {a₁, ...., a_n}。

行空间的概念推广到了在任何域上的矩阵，特别是复数域C。

In linear algebra, the column space C(A) of a matrix A (sometimes called the range of a matrix) is the span (set of all possible linear combinations) of its column vectors.

Let K be a field (such as real or complex numbers). The column space of an m×n matrix with components from K is a linear subspace of the m-space K. The dimension of the column space is called the rank of the matrix. A definition for matrices over a ring K (such as integers) is also possible.