Example · High school
Terms
| Term | This example | Why |
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| basis |
✓ |
The vectors $(1, 0)$ and $(0, 1)$ form a basis of $\reals^2$, because every vector $(x, y)$ is $x (1, 0) + y (0, 1)$, in exactly one way. This basis is the standard basis.
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| linearly independent |
✓ |
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| span |
✓ |
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| orthogonal |
✓ |
The vectors $(1, 0)$ and $(0, 1)$ are orthogonal, because their dot product is $1 \cdot 0 + 0 \cdot 1 = 0$.
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| pairwise linearly independent |
✓ |
The vectors $(1, 0)$ and $(0, 1)$ are pairwise linearly independent, because neither vector is a scalar multiple of the other.
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| orthonormal |
✓ |
The vectors $(1, 0)$ and $(0, 1)$ are orthonormal, because both vectors have length $1$ and their dot product is $0$.
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