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Math 2331 { Linear Algebra

Vector Spaces & SubspacesMath 2331 Linear Vector Spaces & SubspacesJiwen HeDepartment of Mathematics, University of jiwenhe/math2331 Jiwen He, University of HoustonMath 2331, Linear Algebra1 / Vector Spaces & SubspacesVector Spaces Subspaces Determining Vector Spaces & SubspacesVector Spaces: DefinitionVector Spaces: Examples2 2 matricesPolynomialsSubspaces: DefinitionSubspaces: ExamplesDetermining SubspacesJiwen He, University of HoustonMath 2331, Linear Algebra2 / Vector Spaces & SubspacesVector Spaces Subspaces Determining SubspacesVector SpacesMany concepts concerning vectors inRncan be extended to othermathematical can think of avector spacein general, as a collection ofobjects that behave as vectors do inRn. The objects of such a setare SpaceAvector spaceis a nonempty setVof objects, calledvectors, onwhich are defined two operations, calledadditionandmultiplication by scalars(real numbers), subject to the ten axiomsbelow.

A vector space is a nonempty set V of objects, called vectors, on which are de ned two operations, called addition and multiplication by scalars (real numbers), subject to the ten axioms below. The axioms must hold for all u, v and w in V and for all scalars c and d.

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