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evilpostingmong
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Homework Statement
Let U be a fixed nxn matrix and consider the operator T: Msub(n,n)------>Msub(n,n)
given by T(A)=UA.
Show that c is an eigenvalue of T if and only if it is an eigenvalue of U.
Homework Equations
The Attempt at a Solution
If T(A)=UA then T(A)-UA=0 (T-U)A=0.
Let v be an eigenvector of T so Tv=cv.
If v is an eigenvector[tex]\in[/tex]A then A
is not a zero matrix so for (T-U)A=0 we
have Tv-Uv=0 so cv-Uv=0
Uv=cv so c must be an eigenvalue of U for
Uv=Tv=cv and for Uv-Tv=0 for v[tex]\in[/tex]A.