15.2.11  Companion matrix of a polynomial

The companion command finds a matrix given its characteristic polynomial; specifically, if the polynomial is P(x)=xⁿ+a_n−1xⁿ⁻¹+⋯+a₋₁x+a₀, this matrix is equal to the identity matrix of size n−1 bordered with [0,0..,0,−a₀] as first row, and with [−a₀,−a₁,…,−a_n−1] as last column.

• companion takes two arguments:
  • P, a unitary polynomial.
  • x, the name of its variable.
• companion(P,x) returns the matrix whose characteristic polynomial is P.

Examples