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Unformatted text preview: TI ), call it v . So Sv = av for some scalar a C , which is not necessarily itself. But since v comes from null( TI ), we also have Tv = v, so v is also an eigenvector of T . We conclude that two commuting operators have a common eigenvector. Of course, the eigenvalues which correspond to this common eigenvector are not necessarily the same for S and T , but thats okay the important thing is the existence of a common eigenvector. We will see later that this fact, in some ways, explains the way the universe works :) Date : July 9, 2009....
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 Summer '08
 GUREVITCH
 Math, Vector Space

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