Example · Undergraduate
Terms
| Term | This example | Why |
|---|
| vector space |
✓ |
The plane $\reals^2$, with vector addition and multiplication by real numbers, is a vector space over $\reals$.
|
| module |
✓ |
The plane $\reals^2$, with vector addition and multiplication by real numbers, is a module over $\reals$, because every vector space over a field is a module over that field.
|
| algebra (over a field) |
✗ |
The plane $\reals^2$, with only vector addition and multiplication by real numbers, is not an algebra, because no multiplication of two vectors is given.
|
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