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Let T and S be linear transformations of a vector space V, and TS=ST (a) Show that...

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Basic Math

Let T and S be lineartransformations of a vector space V, and TS=ST

(a) Show that Tpreserves the generalized eigenspace and eigenspace of S.

(b) Suppose V is avector space on R and dimV = 4. S has a minimal polynomial of(t-2)2 (t-3)2?. What is the jordan canonicalform of S.

(c) Show that thecharacteristic polynomial of T has at most 2 distinct roots andsplits completely.

Answer & Explanation Solved by verified expert
4.1 Ratings (703 Votes)
a we have Sx x for all x ineigenspace EWe want to show that Tx xNow TS ST TSx STx Tx STx Tx    See Answer
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