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# Definition of codomain of a linear transformation

Put content here**Definition:** The *codomain* of a linear transformation \(T\) is the vector space \(W\) into which the transformation maps its output vectors.
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Notation: If \(T: V \to W\), then \(W\) is the codomain of \(T\).
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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*).
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**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 \(\mathbb{R}^3\).

# Parents

* Terminology