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Linear Transformation
High School
Definition
A function between vector spaces that preserves addition and scalar multiplication.
Formulas
T(\vecu + \vecv) = T(\vecu) + T(\vecv)
Preserves addition
T(c\vecv) = cT(\vecv)
Preserves scalar multiplication
Examples
Example 1
Find the rotation matrix (counterclockwise by θ).
Example 2
Express scaling (2x in x, 3x in y) as a matrix.
Applications
Computer Graphics
Rotation, scaling, translation
Robotics
Coordinate frame transformations
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