Re: help in constructing a binomial consequence

*To*: mathgroup at smc.vnet.net*Subject*: [mg98265] Re: help in constructing a binomial consequence*From*: mark mcclure <mcmcclur at unca.edu>*Date*: Sun, 5 Apr 2009 06:31:31 -0400 (EDT)*References*: <gr4jm9$ac5$1@smc.vnet.net>

On Apr 3, 5:08 am, Galina <Galina.Pil... at gmail.com> wrote: > I need to find an eigenvalues of the matrix M [N*N] where elements > are of the type F[i]*F[j]. I need help to construct the elements F[i] > which must be in the following order: F[1]=1, F[2]=x, F[3]=y, F[4] > =x^2, F[5]=x*y, F[6]=y^2, F[7]=y*x^2, F[8]=x*y^2, F[9]=x^3 an= d etc.... Your pattern seems a bit off. I'm guessing you mean: 1, x, y, x^2, x y, y^2, x^3, x^2 y, x y^2, y^3 In this case, you can define your F like so: biRow[n_] := Table[x^(n - k)*y^k, {k, 0, n}]; Clear[F]; m = 0; Do[F[++m] = binom, {binom, Flatten[Table[biRow[n], {n, 0, 3}]]}]; Then, you can define your matrix via: M = Table[F[i]*F[j], {i, 1, m}, {j, 1, m}]; I'm guessing these matrices all have rank 1. Thus, you can find the only non-zero eigenvalue via: Eigenvalues[M] // Last Mark McClure