projection eigenvector space matlab -

hi have matrix containing 132 elements of 3 features each

a= rand(132,3); 

i compute distance between each element

b=pdist(a); 

and put in squared distance matrix

c = squareform(b); 

i compute eigenvectors of matrix

[v,d] = eig(c); 

now map new element in same space of eigenvectors v.

% take first element of a, assume new 1 new_element = a(1,:); 

i calculate distance other elements of a

d1=pdist2(a(1,:),a); 

now can add row c matrix obtaining

 c2 = squareform([d1,b]) 

what is: given eigenvector space v calculated. can approximate new row of c (i.e first row of c2) in same space (i.e. using eigenvectors of c)?

not sure makes sense...i trying make new classifier, miss last passage because cannot recalculate eigenvectors (calculated using training set)