 The cost of this algorithm is asymptotically O("nk"2) floating point operations, where "n" is the dimensionality of the vectors .If the rows {"v"1, ..., "v""k"} are written as a matrix formula_34, then applying Gaussian elimination to the augmented matrix formula_35 will produce the orthogonalized vectors in place of formula_34.For example, taking formula_37 as above, we have

And reducing this to row echelon form produces

The normalized vectors are then

as in the example above.