Ask for help to solve next problem ( and information where to read more about that ) :

Let's x1,x2,x3,.....,xn are part from real data steam ( n samples may be deterministic or random ). How to construct linearly independent data vectors from the data, and put them into matrix form ? Matrix must represent exactly input data.

I think about construction of n by n correlation matrix, but in this case I loose vector interpretation of data.