Multiplying Basis Sets by Eigenfunctions

[Thomas Markovich]

Hi,

Currently I have a problem for which, after reading all the literature  
I could find, has no apparently solution.

Basically, I am trying to multiply my basis set of functions by my  
matrix of eigenvectors to give me eigenfunctions.

What this looks like is, lets say that I have a set for n=2, I have a  
row vector of

[e^-2*i*x, e^-ix, e^0, e^ix, e^2ix] and I would need to multiply this  
by a matrix of eigenvectors to give me a column vector of  
eigenfunctions. Unfortunately, all I can come up with is to do this by  
hand. Here is what I have tried in Octave.
For n = 5, I do

[EVECT,EIG] = eig(a)
EVECT = (numbers are unimportant, all that matters is that its a 11x11  
matrix)

octave-3.0.2:3> BasisSet =  
[sin(-5.*x),sin(-4.*x),sin(-3.*x),sin(-2.*x),sin(- 
x),sin(0),sin(x),sin(2.*x),sin(3.*x),sin(4.*x),sin(5.*x)]
error: `x' undefined near line 3 column 21
error: evaluating binary operator `.*' near line 3, column 19
error: evaluating argument list element number 1
error: evaluating assignment expression near line 3, column 10
octave-3.0.2:3> x = [-pi,pi];
octave-3.0.2:4> x = [-pi,pi]
x =

   -3.1416   3.1416

octave-3.0.2:5> BasisSet =  
[sin(-5.*x),sin(-4.*x),sin(-3.*x),sin(-2.*x),sin(- 
x),sin(0),sin(x),sin(2.*x),sin(3.*x),sin(4.*x),sin(5.*x)]
BasisSet =

  Columns 1 through 11:

    6.1232e-16  -6.1232e-16  -4.8986e-16   4.8986e-16   3.6739e-16   
-3.6739e-16  -2.4493e-16   2.4493e-16   1.2246e-16  -1.2246e-16    
0.0000e+00

  Columns 12 through 21:

   -1.2246e-16   1.2246e-16   2.4493e-16  -2.4493e-16  -3.6739e-16    
3.6739e-16   4.8986e-16  -4.8986e-16  -6.1232e-16   6.1232e-16

octave-3.0.2:7> BasisSet * EVECT
error: operator *: nonconformant arguments (op1 is 1x21, op2 is 11x11)
error: evaluating binary operator `*' near line 7, column 10
octave-3.0.2:7> BasisSet .* EVECT
error: product: nonconformant arguments (op1 is 1x21, op2 is 11x11)
error: evaluating binary operator `.*' near line 7, column 10


 From here, I have no clue where to go. I am honestly not even sure if  
octave can do what I need it to do. Anyways, any help in any fashion  
is much appreciated.