@Rouben Rostamian  Dear Rouben it is just an error because the matrix is square that is mean m=n 

the diagonal is not included
we suppose that there is one small element

@Kitonum thank mr kitnoum but the question is by using f

@Kitonum thank you Mr kitonum but this method doesn't work for me here the error that maple gives to me:

> P := proc (x) options operator, arrow; x^4+x^3+a*x^2+sqrt(2)*x+b end proc;
      4    3      2                
x -> x  + x  + a x  + sqrt(2) x + b
> solve(evalc(([Re, Im])(P(1+I))) = `~`[0, 0]);
Error, (in solve) invalid arguments
> solve(eval(P(x), %));
Error, invalid input: eval received proc (x) options operator, arrow; x^4+x^3+a*x^2+sqrt(2)*x+b end proc, which is not valid for its 2nd argument, eqns
 

@acer thank you very much, for your help

yes i'm trying to deduce the sign of the root of my polynomial, is there any  way to just simplify these expressions, such as {I[f], I[r], Lambda[r], N[H], N[f], S[H], S[r], b[Hf], b[fH],
   b[fr], b[rf], beta[fH], beta[fr], beta[Hf], beta[rf],
   lambda[H], mu[B], mu[H], mu[f], mu[rd], tau[H]} are all positifs

@tomleslie my question is to get a way to simplify these coefficients in order to learn their sign , is there ?

@tomleslie thank you mister Tomleslie for your answer, i'm searshing if there is a method to simplify the coefficients of my characteristic polynomial to learn their sign under the assumption that all the parameters are positifs , can you help me please !

stab.mw@Carl Love  i did it but it is very diffecult to verify the résult can you help me please !

@Rouben Rostamian  i want the exact value because i want to discuss the sign of these values 

but maple doesn't give me the values

@Mariusz Iwaniuk  thank you for your response but in this way , maple will give me a very complicated results, can you help me to simplify it ?

@Kitonum thank you very much, now it is more clear for me.

@Kitonum  but here we have recurrente relation u(n+1)=sin(u(n)) , i can't understand because in your example is the composition functions ?

@Kitonum can you explain to me with examples how the repeated operator @@ works   ?

@Kitonum thank you mr kitonum for your help but if we calculate u(1) if we replace n=0 we get sin(1.5)=0.99.... not 0.84...

@vv thank you for your clarification , but if you chosse as example sqrt(x)+2*x+3/sqrt(2*x+1) , maple can't simplify this , this why i want to understand this case !