| 单词 | Row space |
| 释义 |
Row space
中文百科
行空间与列空间 Row and column spaces（重定向自Row space）
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, ...., an]，则Col A = Span {a1, ...., an}。 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。
英语百科
Row and column spaces 行空间与列空间（重定向自Row space）
 ![The column vectors of a matrix. The column space of this matrix is the vector space generated by linear combinations of the column vectors.
In linear algebra, the row space of a matrix is the set of all possible linear combinations of its row vectors. Let K be a field (such as real or complex numbers). The row space of an m × n matrix with components from K is a linear subspace of the n-space Kn. The dimension of the row space is called the row rank of the matrix.[1]
A definition for matrices over a ring K (such as integers) is also possible.[2]
vector space generated by linear combinations of the column vectors.](/uploads/202502/08/Matrix_Columns.svg2631.png) 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. |
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