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# Linear Algebra : Complex Vector Space and Eigenvalues

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This is problem #15 on page 189 of Axler's book Linear Algebra Done Right.

Suppose V is a complex vector space. Suppose T is in L(V) is such that 5 and 6 are eigenvalues of T and that T has no other eigenvalues.
Prove that (T &#8722; 5I)^(n&#8722;1)*(T &#8722; 6I)^(n&#8722;1) = 0, where n = dimV.

##### Solution Summary

A Complex Vector Space and its Eigenvalues are investigated.

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