- #1
Ylle
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Homework Statement
Let pA(x) and pB(x) be the characteristic polynomial for A and B. If B is similar to A, then there exists a non-singular matrix S so B = S-1AS. Thus there:
pB(x) = det(B-[tex]\lambda[/tex]I)
= det(S-1AS-[tex]\lambda[/tex]I)
= det(S-1(A-[tex]\lambda[/tex]I)S)
= det(S-1)det(A-[tex]\lambda[/tex]I)det(S)
= pA(x)
Homework Equations
The Attempt at a Solution
My question is, that I really don't know why the 3rd step is legal ? Can I just put the S's anywhere I want ?
Regards