Math 2331 { Linear Algebra - UH

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.

1 To show that H is a subspace of a vector space, use Theorem 1. 2 To show that a set is not a subspace of a vector space, provide a speci c example showing that at least one of the axioms a, b or c (from the de nition of a subspace) is violated. Jiwen He, University of Houston Math 2331, Linear Algebra 18 / 21

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