Extensions of differential fields. I, II (Q2652499)

It is shown how the elements of an elementary operation matrix \(\underset{\tilde{}}{L}\) which transforms a positive-definite matrix \(A\) into a diagonal matrix \(D\) (using a Gaussian elimination procedure), increase when the order of \(\underset{\tilde{}}{A}\) increases by adding rows and columns to the original matrix. Three theorems are proved.