On 6/15/10 6:21 AM, Minh Nguyen wrote:
As you can see, these two characteristic polynomials differ in only their signs. One can be obtained from the other by multiplying through by -1. What I would like to know is: Is there some reason for this inconsistency? Or are the two characteristic polynomials above "essentially" the same?
One is computed using x*Id-M, the other by M-x*Id. This will lead to a sign difference for odd-sized matrices. In my graduate abstract algebra course, we defined the characteristic polynomial using x*Id-M specifically so that we'd always have a monic polynomial as the output.
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