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[ adjective ] equal to zero when raised to a certain power
Used in print (Kenneth Hoffman and Ray Kunze, Linear Al...)We say that N is nilpotent if there is some positive integer r such_that * * f . Then there is a diagonalizable operator D on V and a nilpotent operator N on V such_that ( a ) * * f , ( b ) * * f . The diagonalizable operator D and the nilpotent operator N are uniquely determined by ( a ) and ( b ) and each of them is a polynomial in T . We have just observed that we can write * * f where D is diagonalizable and N is nilpotent , and where D and N not_only commute but are polynomials in T . Now suppose that we also have * * f where D ' is diagonalizable , N ' is nilpotent , and * * f . Related terms |
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