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Unformatted text preview: Vector Space Deﬁnition
A vector space V over a ﬁeld of scalars F : • Binary operation + on V • Scalar multiplication: for all x ∈ V and α ∈ F , αx ∈ V For all (1) (2) (3) (4) (5) (6) (7) (8) x, y, z ∈ V and all α, β ∈ R, + is commutative + is associative + has an identity 0 every x ∈ V has an inverse for +, written −x. α(x + y ) = αx + αy (α + β )x = αx + βx (αβ )x = α(βx) 1·x=x ...
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