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
- Watch the video lecture Linear Transformations and their Matrices (00:49:27)
Lecture 30: Linear Transformations and their Matrices
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 7.1 in the 4th edition or Section 8.1 in the 5th edition.
Problem Solving Video
- Watch the recitation video on Linear Transformations (00:10:46)
Problem Solving: Linear Transformations
- Recitation video transcript (PDF)
Problems and Solutions
Work the problems on your own and check your answers when you're done.