Row and column spaces
Vector spaces associated to a matrix
Row and column spaces
In linear algebra, the column space (also called the range or image) of a matrix A {\displaystyle 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 F {\displaystyle F} be a field. The column space of an m × n {\displaystyle m\times n} matrix with components from F {\displaystyle F} is a linear subspace of the m-space F m {\displaystyle F^{m}} . The dimension of the column space is called the rank of the matrix and is at most min { m , n } {\displaystyle \min\{m,n\}} . A definition for matrices...
Read on Wikipedia · Image Jim.belk, Public domain
Open boosters, collect cards and trade them. Free to play.
Play for free