theorem Th38: :: VECTSP11:38

for n being Nat
for K being Field
for V1 being VectSp of K
for f being linear-transformation of V1,V1
for L being Scalar of K st n >= 1 holds
ex h being linear-transformation of V1,V1 st
( (f + (L * (id V1))) |^ n = (f * h) + ((L * (id V1)) |^ n) & ( for i being Nat holds (f |^ i) * h = h * (f |^ i) ) )