@John Fredsted 

Yes, sure. My matrix is:

U := <<(1/2)*sqrt(2), (1/4)*sqrt(2), (1/5)*sqrt(5), 0, -I*sqrt(2)*(1/4), I*sqrt(5)*(1/10)>|<u1112, u1122, u1132, u2112, u2122, u2132>|<u1113, u1123, u1133, u2113, u2123, u2133>|<0, I*sqrt(2)*(1/4), -I*sqrt(5)*(1/10), 1/2, (1/4)*sqrt(2), 3*sqrt(5)*(1/10)>|<u1212, u1222, u1232, u2212, u2222, u2232>|<u1213, u1223, u1233, u2213, u2223, u2233>>

Where uijkl are the values that can vary as long as it is unitary. and columns 1 and 3 are the fixed ones. Anyway, I managed to solve it with GramdSchimdt, as @vv suggested.

Thanks anyway!:)

@Kitonum 

Thanks for the answer! but LeastSquares did'nt help, as I had to operate with matrices and Least squares uses a matrix and two vectors... I needed something like A.x=B where A and B are both matrices while LeastSquares evaluates for A matrix and B vector.

Thank you for helping, anyway!:)

@vv 

Thank you! This actually worked!... I should have figured it out hehe

Thanks !:)