Notes
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A vector space, or linear space, is a set of vectors. It's possible to scale by numbers, called scalars, and add these vectors together.
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The operations of vector addition or scalar multiplication in a vector space must safisty the following axions:
- Additive axions. For every , , and in , we have:
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- Multiplicative axions. For every in , and real numbers and , we have:
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- Distributive axions. For every and in , and real numbers and , we have:
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- Additive axions. For every , , and in , we have: