# Definition of image (of a point) under a linear transformation

Put content here**Definition:** The *image* of a vector \(\mathbf{v}\) under a linear transformation \(T: V \to W\) is the output vector \(T(\mathbf{v}) \in W\).
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Notation: \(T(\mathbf{v})\) or \(\mathbf{w} = T(\mathbf{v})\).
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This is the result of applying the transformation to a specific input vector.
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**Example:** If \(T: \mathbb{R}^2 \to \mathbb{R}^2\) is defined by \(T(x,y) = (2x, y)\), then the image of \((3,4)\) under \(T\) is \(T(3,4) = (6,4)\).

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* Terminology