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_sqttq5t3Opd0-5R4VjgLnyA0Ao6VjoHOo5JjXqZ8uqm-DQ4zG6mxDMOqAik53oalNZL7BRMv2QQLgN8AdQcp4pcn4F64-2YfmcgLvU86iB6RSc6ox-34t6B_ke34UEdUhib99pJ6wnkURc8dNdHdZiVuYtzRA=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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