Linear Algebra › Section D · Vector spaces › Topic D.1
Vector spaces and subspaces
Arrows in the plane are not the only things you can add and scale. Polynomials, matrices, functions and signals obey the same algebra, and naming that shared structure, a vector space, lets one set of theorems work for all of them.
In this topic
- The same algebra everywhere
- The definition
- A gallery of vector spaces
- Facts that follow from the rules
- Subspaces
- Worked example: a subspace of polynomials
- Worked example: two sets that fail
- Spans are subspaces
- Subspaces you can picture
- Common mistakes to avoid
- Key takeaways
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