Vector Space Definitions

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10 Terms

1
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Closure Property of Addition

If x∈V and y∈V, then x+y∈V

2
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Commutative Property

x+y=y+x

3
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Associative Property

x+(y+z)=(x+y)+z

4
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Additive Identity Property

∃0∈V such that x+0=x, ∀x∈V

5
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Additive Inverse Property

∀x∈V∃(-x)∈V such that x+(-x)=0

6
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Closure Property of Scalar Multiplication

If α∈R and x∈V, then αx∈V

7
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Vector Distributive Property

α(x+y)=αx+αy

8
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Scalar Distributive Property

(α+β)x=αx+βx

9
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Scalar Associative Property

α(βx)=(αβ)x

10
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Scalar Identity Property

1x=x