The companion matrix to a
monic polynomial
 |
(1)
|
is the
square
matrix
![A=[0 0 ... 0 -a_0; 1 0 ... 0 -a_1; 0 1 ... 0 -a_2; | | ... ... |; 0 0 ... 1 -a_(n-1)]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uGn4eVf6QaayWIyQDaNcv_AFbdjfhIw4SNYkODRX7DyGU_cWfWoQ-l8ob6eDaKBjfAsGv9gfaCrwuBmHuFn2EnDvh-vDC84hlWRjuE3vJyKjf1GRswB9QmdsLC4LBp5a-Wg_CjM_hsxu_eC3teSdVsu0f9xCI=s0-d) |
(2)
|
with ones on the
subdiagonal and the last column given by the coefficients of

. Note that
in the literature, the companion matrix is sometimes defined with the rows and columns
switched, i.e., the
transpose of the above matrix.
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