next up previous contents index
suivant: Hessenberg matrix reduction : monter: Matrix reduction précédent: Adjoint matrix : adjoint_matrix   Table des matières   Index

Companion matrix of a polynomial : companion

companion takes as argument an unitary polynomial P and the name of its variable.
companion returns the matrix whose characteristic polynomial is P.
If P(x) = xn + an-1xn-1 + ... + a-1x + a0, this matrix is equal to the unit matrix of size n - 1 bordered with [0, 0.., 0, - a0] as first row, and with [- a0, - a1,...., - an-1] as last column.
Input :
Output :
Input :
Output :

giac documentation written by Renée De Graeve and Bernard Parisse