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Jonathanlam
Joined: 26 Jan 2004Posts: 14
Location: Hong Kong
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Posted: Tue Jan 27, 2004 6:05 pm Post subject: Linear Algebra
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Let a,b be endomorphism of a linear space X.Prove that if X is finite-dimensional then ab-ba not equals the identity map.Thanks.
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aRdolf
Frequent VisitorJoined: 18 Jan 2004Posts: 37
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Posted: Tue Jan 27, 2004 8:25 pm Post subject:
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Let A, B be invertible matrices,
then tr(AB-BA)=trAB-trBA=trAB-trAB=0, not equal to n=dimension.
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aRdolf
Frequent VisitorJoined: 18 Jan 2004Posts: 37
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Posted: Tue Sep 14, 2004 11:28 am Post subject:
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I wonder if this result is true for infinite dimensional spaces. The trace works well for trace class operators in Hilbert Space.
How about arbitrary endomorphisms on Banach Spaces?
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