When we multiply a matrix by an input vector we get an output vector, often in a new space. We can ask what this "linear transformation" does to all the vectors in a space. In fact, matrices were originally invented for the study of linear transformations.
Lecture Video and Summary
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Linear Transformations and their Matrices (00:49:27)
Lecture 30: Linear Transformations and their Matrices
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- Lecture video transcript (PDF)
- Read Section 7.1 in the 4th edition or Section 8.1 in the 5th edition.
Problem Solving Video
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Linear Transformations (00:10:46)
Problem Solving: Linear Transformations
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Problems and Solutions
Work the problems on your own and check your answers when you're done.