|Sep29-11, 10:38 PM||#1|
characteristic polynomial coefficients
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
|Sep29-11, 11:27 PM||#2|
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.
|Similar Threads for: characteristic polynomial coefficients|
|coefficients of characteristic polynomial||Linear & Abstract Algebra||2|
|Characteristic Polynomial of A and A^2||Calculus & Beyond Homework||4|
|Coefficients of characteristic polynomial (linear algebra)||Calculus & Beyond Homework||1|
|characteristic polynomial||Linear & Abstract Algebra||3|
|characteristic polynomial||Linear & Abstract Algebra||2|