**Definition:** The *codomain* of a linear transformation \(T\) is the vector space \(W\) into which the transformation maps its output vectors.

Notation: If \(T: V \to W\), then \(W\) is the codomain of \(T\).

The codomain specifies the *type* of output vectors. It may be larger than the actual set of outputs (which is called the *range* or *image*).

**Example:** For \(T: \mathbb{R}^2 \to \mathbb{R}^3\) defined by \(T(x,y) = (x, y, 0)\), the codomain is \(\mathbb{R}^3\), but the range is only the \(xy\)-plane within \(\mathbb{R}^3\).