One can set the proportionality factor to be equal to one when |A|+|I|\leqslant 1, which fixes this factor for other values of A and I due to the relations (2.17). It is explicitly spelled out in e.g. [41]. There exists a different choice of normalizations that simplifies this ex...
The routines just written enable you to compute the LU decomposition of any type of matrix. For certain types, however, we have extremely efficient decomposition functions already coded in the Lapack package. It only makes sense to call these routines when possible, and the MATH library provides...