Example · High school
Terms
| Term | This example | Why |
|---|
| pairwise linearly independent |
✓ |
The vectors $(2, 0)$ and $(0, 2)$ are pairwise linearly independent, because neither vector is a scalar multiple of the other.
|
| linearly independent |
✓ |
The vectors $(2, 0)$ and $(0, 2)$ are linearly independent, because $a (2, 0) + b (0, 2) = (2a, 2b)$ is the zero vector only if $a = b = 0$.
|
| orthogonal |
✓ |
The vectors $(2, 0)$ and $(0, 2)$ are orthogonal, because their dot product is $2 \cdot 0 + 0 \cdot 2 = 0$.
|
| orthonormal |
✗ |
The vectors $(2, 0)$ and $(0, 2)$ are not orthonormal, because both vectors have length $2$, not $1$; dividing each vector by $2$ gives the orthonormal vectors $(1, 0)$ and $(0, 1)$.
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