Linear Algebra › Section A · Linear equations in linear algebra › Topic A.9
The matrix of a linear transformation
Every linear transformation between coordinate spaces is secretly a matrix, and you can find that matrix just by watching where the standard unit vectors go. Once you have it, questions about the transformation become questions about pivots.
In this topic
- From a description to a matrix
- The standard matrix
- Worked example: the rotation matrix
- Reflections
- Scalings, shears and projections
- Worked example: one move after another
- Onto and one-to-one
- Tests through the standard matrix
- Worked example: onto but not one-to-one
- Common mistakes to avoid
- Key takeaways
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