Linear Algebra › Section D · Vector spaces › Topic D.2
Null spaces, column spaces, and kernels
Every matrix carries two subspaces: the vectors it sends to zero and the vectors it can produce. For a general linear transformation they become the kernel and the range, and together they decide whether the map is one-to-one or onto.
In this topic
- Two subspaces from every matrix
- The null space
- Worked example: an explicit description of Nul A
- The column space
- Worked example: testing membership
- Contrasting the two spaces
- Kernel and range of a linear transformation
- Worked example: differentiation
- One-to-one, onto and isomorphisms
- Common mistakes to avoid
- Key takeaways
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