$(3, -1)$ is the coordinate vector of $3 + 2x$, relative to the basis $(1 + x, x)$
Terms
| Term | This example | Why |
|---|---|---|
| coordinate vector | ✓ | $3 + 2x$ is the linear combination of the basis vectors $1 + x$ and $x$ using the coefficients $3$ and $-1$: \(3 + 2x = 3(1 + x) + (-1)(x)\) |
Distinctions using this example
- Vector vs. coordinate vector: The same vector $3 + 2x$ has different coordinates in a different basis.