Unformatted text preview: set { T ( v k +1 ) ,...,T ( v n ) } is a basis for R ( T ). Now extend this to an ordered basis γ := { w 1 ,...,w k ,T ( v k +1 ) ,...,T ( v n ) } for W . Then [ T ( v j )] γ = ± if 1 ≤ j ≤ k e j if k + 1 ≤ j ≤ n and so [ T ] γ β = ··· . . . . . . . . . 1 . . . ··· 1 is diagonal, as desired. References Friedberg, et. al. Linear Algebra. Department of Mathematics, University of California, Los Angeles, 90095 Email address : [email protected] 1...
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 Fall '09
 Jones
 Linear Algebra, Algebra, Vector Space, ordered basis, Friedberg

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