Question

define column space?​

Answer 1

In linear algebra, the column space of a matrix A is the span of its column vectors. The column space of a matrix is the image or range of the corresponding matrix transformation. Let be a field. The column space of an m × n matrix with components from is a linear subspace of the m-space.

Answer 2

Answer:

In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix is the image or range of the corresponding matrix transformation.

Let {\displaystyle \mathbb {F} } \mathbb {F} be a field. The column space of an m × n matrix with components from {\displaystyle \mathbb {F} } \mathbb {F} is a linear subspace of the m-space {\displaystyle \mathbb {F} ^{m}} {\displaystyle \mathbb {F} ^{m}}. The dimension of the column space is called the rank of the matrix and is at most min(m, n).[1] A definition for matrices over a ring {\displaystyle \mathbb {K} } \mathbb {K} is also possible.

The row space is defined similarly.

This article considers matrices of real numbers. The row and column spaces are subspaces of the real spaces Rn and Rm respectively.[2]

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