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_v6-IBAAOqZmvR4ckjoK8XdjHKIH1jRGuuWeOnMtNENxkr3fAZ8euXA_uwbhfrq8JGCfc_DPVAlnGeVfz-1tQofpXqOuLMa6eRTH7_3RCh9es9C1q4wRknTmn77kAtWxZBxJJ_w8tVMKXcFb8k8TAjVDF2wM90=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.
No comments:
Post a Comment