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Unformatted text preview: (4) Show that t R n ⊗ M n ( R ) R n ∼ = R , an isomorphism of ( R,R )bimodules. (5) Show the following isomorphisms of Ralgebras: (a) C ⊗ R C ∼ = C ⊕ C (b) H ⊗ R C ∼ = M 2 ( C ) (c) H ⊗ R H ∼ = M 4 ( R ) where R , C , and H denote the real numbers, the complex numbers, and the quaternions, respectively. (6) (The exercise on the “Cliﬀord Algebras” handout). Show that Cliﬀ (2 , 0) ∼ = M 2 ( R ) and that Cliﬀ (0 , 2) ∼ = H ....
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This note was uploaded on 08/06/2008 for the course MATH 220 taught by Professor Morrison during the Spring '08 term at UCSB.
 Spring '08
 MORRISON
 Algebra, Vectors, Matrices

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