where "Iλ" is the identity operator on "Vλ". The above matrix would be upper-triangular except for the "A"22 block. But exactly the same procedure can be applied to the sub-matrix "A"22, viewed as an operator on "Vλ"⊥, and its submatrices. Continue this way until the resulting matrix is upper triangular. Since each conjugation increases the dimension of the upper-triangular block by at least one, this process takes at most "n" steps. Thus the space C"n" will be exhausted and the procedure has yielded the desired result.