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