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# 10 Axioms of vector spaces

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if u and v are objects in V, then u+v is in V
1
u+v = v+u
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u+(v+w) = (u+v)+w
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There is an object 0 in V called a zero vector for V,
Such that 0+u = u+0 = u
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For each u in V, there is an object -u in V, called a negative of u, such that u+(-u) = (-u)+u = 0
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If k is any scalar and u is any object in V, then ku is in V.
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k(u+v) = ku + kv
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(k+m)u = ku+mu
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k(mu) = (km)(u)
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1u = u
10

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