Learning Outcomes
How can we understand linear maps algebraically?
By the end of this chapter, you should be able to...
- Determine if a map between Euclidean vector spaces is linear or not.
- Translate back and forth between a linear transformation of Euclidean spaces and its standard matrix, and perform related computations.
- Compute a basis for the kernel and a basis for the image of a linear map, and verify that the rank-nullity theorem holds for a given linear map.
- Determine if a given linear map is injective and/or surjective.
- Explain why a given set with defined addition and scalar multiplication does satisfy a given vector space property, but nonetheless isn’t a vector space.
- Answer questions about vector spaces of polynomials or matrices.
