Linear Vector Spaces Exam 1

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9 Terms

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Addition Properties that must be satisfied for a vector space

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Scalar Multiplication Properties that must be satisfied for a vector space,

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Subspaces: M subset of V is a subspace if

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Norms: A norm ||.|| on vector space V satisfies: 

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Inner Products: An inner product <.,.> on V satisfies:

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Linear Independence/Dependence: Set S = {v_1, …, v_n} is

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Span {v_1, …, v_n} is always a

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S is Linearly Dependent iff

at least one vector is a linear combination of the others

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Rank-Nullity Theorem

dim(V) = dim(Ker(T)) + dim(R(T))