Given a monic polynomial the companion matrix of , denoted , is the matrix with ’s down the first subdiagonal and minus the coefficients of down the last column, or alternatively, as the transpose of this matrix. Adopting the first convention this is simply
Regardless of which convention is used the minimal polynomial (http://planetmath.org/MinimalPolynomialEndomorphism) of equals , and the characteristic polynomial of is just . The is needed because we have defined the characteristic polynomial to be . If we had instead defined the characteristic polynomial to be then this would not be needed.
|Date of creation||2013-03-22 13:17:12|
|Last modified on||2013-03-22 13:17:12|
|Last modified by||aoh45 (5079)|