Linear Algebra › Section A · Linear equations in linear algebra › Topic A.8
Introduction to linear transformations
So far a matrix has been a table of coefficients. Now it becomes a machine that takes in a vector and returns another, and the machines that respect addition and scaling, the linear transformations, turn out to be the heart of the subject.
In this topic
- Matrices that act
- Transformations and their vocabulary
- Matrix transformations
- Worked example: images and pre-images
- Two geometric examples
- Linear transformations
- Consequences of linearity
- Spotting non-linear maps
- Worked example: using linearity
- Linearity beyond Rⁿ
- Common mistakes to avoid
- Key takeaways
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