14.2.11 Companion matrix of a polynomial
The companion
command finds a matrix given its characteristic
polynomial; specifically, if the polynomial is
P(x)=xn+an−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,…,−an−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
companion(x^4+3x^3+2x^2+4x-1,x) |