suivant: Minimal polynomial : pmin
monter: Matrix reduction
précédent: Characteristic polynomial : charpoly
Table des matières
Index
Characteristic polynomial using Hessenberg algorithm :
pcar_hessenberg
pcar_hessenberg takes as argument a square
matrix A of size n and optionnaly the name of a symbolic variable.
pcar_hessenberg returns the characteristic polynomial P of A written
as the list of its coefficients if no variable was provided
or written in its symbolic form with respect to the variable name given
as second argument, where
P(x) = det(xI - A)
The characteristic polynomial is computed using the Hessenberg algorithm
(see e.g. Cohen) which is more efficient (O(n3) deterministic) if
the coefficients of A are in a finite field or use a finite
representation like approximate numeric coefficients. Note however that
this algorithm behaves badly if the coefficients are e.g. in
.
Input :
pcar_hessenberg([[4,1,-2],[1,2,-1],[2,1,0]] % 37)
Output :
[1 % 37 ,-6% 37,12 % 37,-8 % 37]
Input :
pcar_hessenberg([[4,1,-2],[1,2,-1],[2,1,0]] % 37,x)
Output :
x^
3-6 %37 *x^
2+12 % 37 *x-8 % 37
Hence, the characteristic polynomial of [[4,1,-2],[1,2,-1],[2,1,0]] in
/37
is
x3 -6x2 + 12x - 8
suivant: Minimal polynomial : pmin
monter: Matrix reduction
précédent: Characteristic polynomial : charpoly
Table des matières
Index
giac documentation written by Renée De Graeve and Bernard Parisse