A basis is a set of vectors, as few as possible, whose combinations produce all vectors in the space. The number of basis vectors for a space equals the dimension of that space.
Lecture Video and Summary
- Watch the video lecture Independence, Basis and Dimension (00:50:14)
Independence, Basis and Dimension
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 3.5 in the 4th edition or Section 3.4 in the 5th edition.
Problem Solving Video
- Watch the recitation video on Basis and Dimension (00:08:09)
Basis and Dimension
- Recitation video transcript (PDF)
Problems and Solutions
Work the problems on your own and check your answers when you're done.