Unformatted text preview: X i =1 i = 1 1 Now, let T : R R be a linear transformation with R regarded as a Qvector space (i.e. T is additive, and homogeneous with respect to rational scalars). Then: X i =1 T ( i ) = T 1 1 [NOTE: Lets say that a real number r is transcendental i 6 p ( x ) P ( Q )( p ( r ) = 0). If necessary, you may use, without proof, the fact that is transcendental.] 6. If A and B are ( m n ) and ( n m )matrices, respectively, then even though AB and BA have dierent dimensions, both are square, and det( AB ) = det( BA )....
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 Fall '08
 GUREVITCH
 Math, Vector Space, linear transformation

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