Orthogonalize in a discrete setting

*To*: mathgroup at smc.vnet.net*Subject*: [mg110567] Orthogonalize in a discrete setting*From*: J Davis <texasautiger at gmail.com>*Date*: Sat, 26 Jun 2010 03:09:29 -0400 (EDT)

I am trying to implement Orthogonalize in a particular scenario. First, I have L=3; pts=Table[n,{n,1,L}]; f[z_,n_]:=Product[1+z Part[pts,m],{m,1,n-1}] The z argument above will be taken from a list of complex numbers which I named zees (which also has length L), so z[i_]:=Part[zees,i] I want to orthogonalize {f[z[1],n],f[z[2],n],f[z[3],n]} with respect to the discrete inner product Sum[u[k] Conjugate[v[k]] Part[pts,k],{k, 1,L}] so I tried Orthogonalize[Table[f[z[i],n],{i,1,L}],Sum[#1 #2 Part[pts,k],{k, 1,L}]&] and other variations to no avail. What is the proper way to pass the functions/vectors to be orthgonalized in this setting? And then, what is the proper way to set up the inner product function based on the former? Thanks for any help, JD