Let V and W be a vector space. dimW=m, dimV=n, and the linear transformations:

T:V-->W

S:W-->V

Need to prove that p (characteristic polynomial) has:

p(SoT) = p(ToS)*x^(m-n)

when "o" means a composition.

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- Apr 6th 2010, 03:59 AMAlso sprach ZarathustraVector space,linear transformations & char. polynomials.
Let V and W be a vector space. dimW=m, dimV=n, and the linear transformations:

T:V-->W

S:W-->V

Need to prove that p (characteristic polynomial) has:

p(SoT) = p(ToS)*x^(m-n)

when "o" means a composition.