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

Created over 8 years ago, updated 10 days ago

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).

Notation: (T(\mathbf{v})) or (\mathbf{w} = T(\mathbf{v})).

This is the result of applying the transformation to a specific input vector.

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)).