# Definition of domain of a linear transformation

Put content here**Definition:** The *domain* of a linear transformation \(T\) is the vector space \(V\) from which the transformation takes its input vectors.
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Notation: If \(T: V \to W\), then \(V\) is the domain of \(T\).
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Every vector in the domain must be mapped to exactly one vector in the codomain. The domain is the entire source vector space, not just a subset.
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**Example:** For the transformation \(T: \mathbb{R}^3 \to \mathbb{R}^2\) defined by \(T(x,y,z) = (x+y, z)\), the domain is \(\mathbb{R}^3\). Any vector in \(\mathbb{R}^3\) can serve as input to \(T\).

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