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Unformatted text preview: set { T ( v k +1 ) ,...,T ( v n ) } is a basis for R ( T ). Now extend this to an ordered basis := { w 1 ,...,w k ,T ( v k +1 ) ,...,T ( v n ) } for W . Then [ T ( v j )] = if 1 j k e j if k + 1 j n and so [ T ] = . . . . . . . . . 1 . . . 1 is diagonal, as desired. References Friedberg, et. al. Linear Algebra. Department of Mathematics, University of California, Los Angeles, 90095 Email address : ethan@math.ucla.edu 1...
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This note was uploaded on 10/20/2010 for the course MATH MAT443 taught by Professor Jones during the Fall '09 term at ASU.
 Fall '09
 Jones
 Linear Algebra, Algebra, Vector Space

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