Real Matrix Range

Why

When we think of a matrix $A$ as giving a linear function, then we refer it is natural to speak of the range of the matrix when referencing the range of the function.

Definition

The range of a real matrix $A \in \R ^{m \times n}$ is the range of the function $f: \R ^n \to \R ^m$ defined by $f(x) = Ax$. The range is a subspace of $\R ^n$.