Leverrier method to find polynomial of matrix

Hi guys,

I need to find a method to generalize Leverrier Method to find matrix's characteristic polynomial.

Input should be only the matrix.

As theory I have:

1. PA(x)=x^n-c1*n^(n-1)+c2*x(n-2)+...+(-1)^n*c[n] - polynomial
2. s[k]=trace(A^k), 1<=k<=n
3. c[k], 1<=k<=n

c1=s1

c2=(s1*c2-s[k])/2

c[k]=(s1*c[k-1]-s2*c[k-2]+...+(-1)^(k+1)*s[k])/k, 2<=k<=n

Also i have to display PA and a graph or something

What I have so far:

function [A,n]=leverrier_n()

for i=1 to n

for j=2 to n

V[j]=A^j

s[i]=trace(V[j])

end

end

for k=2 to n

i=1;

t[1]=s[1]

t[k]=(s[i]*t[k-1]-s[i+1]*t[k-2]+)/k

end

end

Answer 1

[David Hill]

function c = leverrier(A)
    a=size(A,1);
    M=zeros(a);
    c=zeros(1,a+1);
    c(1)=1;    
    for k=2:a+1
        M=A*M+c(k-1)*eye(a);
        c(k)=-1/(k-1)*trace(A*M);
    end
end

[qUser Userq]

Thank you so much!