I am reading about
LU factorization for the first time. I encounter a theorem that says that if we can obtain a Upper-triangular row equal matrix
U from matrix
A with elementary matrices call them
E1, E2, .., Ek that are not row interchanged then we can have
LU factorization. The reason for not interchanging rows as said is to keep
Ei matrices Lower-Triangular. I think if We never interchange rows but for example Add s times of row 2 to row 1 We contract the Lower-triangularity of
Ei matrices too, but this operator didn't forbid in the theorem as you see.
Thank You in Advance.