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Unformatted text preview: Q T .˛.v C N// D Q T .˛v C N/ D T.˛v/ D ˛T.v/ D ˛ Q T .v C N/: n Proposition 3.3.14. (Diamond Isomorphism Theorem for Vector Spaces) Let A and N be subspaces of a vector space V . Let ± denote the quotient map ± W V ! V=N . Then ± ± 1 .±.A// D A C N is a subspace of V containing both A and N . Furthermore, .A C N/=N Š ±.A/ Š A=.A \ N/ . Proof. Exercise 3.3.8 . n Bases and dimension We now consider span, linear independence, bases and dimension for abstract vector spaces....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Vector Space

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