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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.

second entry is and therefore the sum of two vectors in H is also in H: (H is closed under addition) c. Multiplying a vector in H by a scalar produces another vector in H (H is closed under scalar multiplication). Since properties a, b, and c hold, V is a subspace of R3. Jiwen He, University of Houston Math 2331, Linear Algebra 11 / 21

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