Unformatted text preview: ical form of a matrix proceeds by ﬁrst computing the rational canonical form and then applying the primary decomposition to the generator of each cyclic submodule. Let A be a matrix in Mat n .K/ whose characteristic polynomial factors into linear factors in KŒxŁ . Let T be the linear operator of left multiplication by A on K n . Suppose we have computed the rational canonical form of A (by the method of the previous section). In particular, suppose we have a direct sum decomposition .T;K n / D .T 1 ;V 1 / ˚ ²²² ˚ .T s ;V s /; where V j is a cyclic KŒxŁ –submodule with generator v .j/ and period a j .x/ , where a 1 .x/;:::;a s .x/ are the invariant factors of A ....
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 Fall '08
 EVERAGE
 Linear Algebra, Algebra, Multiplication, Jordan Canonical Form, Ues, aj .x/

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