Question 9439: , show that a characterestic polynomial is always monic.
please help me solving the above problem.
thank you
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! You should mention about your definition of characteristic polynomial.
Is it about a linear operator a square matrix, etc?
You cannot assume study the same material or textbook as you right now.
In general, char(T) or char(A) = det(xI - T) or det(xI - A)
and very clearly the leading coefficient is 1 and so it is monic.
You may need to use similar matrices i.e.
det(xI - A) = det(xI - P^-1 B P) = det(P^-1)det(xI - B) det(P)
= det(xI - B)
Kenny
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