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Characteristic polynomial coefficients 
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#1
Sep2911, 10:38 PM

P: 140

For any characteristic polynomial determined from A  eI (where A is a nxn matrix, e is an eigenvalue and I is the identity matrix),
is it a rule that the coefficient associated with the char. polynomail term of highest degree must be positive ? My tutor made a theory that if the characteristic polynomial's coefficient of highest power is negative, then divide it through by 1 to make it positive. Im not sure why it has to be positive, so I'd really like some clarification thanks 


#2
Sep2911, 11:27 PM

Sci Advisor
HW Helper
P: 9,453

there is no rule on this. there is an annihilator ideal and the characteristic polynomial is any generator, so the first coefficient could almost be anything. i usually like it to be positive. but if you define it to be a certain determinant t could be either. this is not at all important for applications.



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