theorem Th28: :: MATRIXJ2:28

for K being Field
for V1, V2 being finite-dimensional VectSp of K
for b1 being OrdBasis of V1
for b2 being OrdBasis of V2
for L being Element of K st len b1 = len b2 holds
for F being linear-transformation of V1,V2 st ( for i being Nat holds
( not i in dom b1 or F . (b1 /. i) = L * (b2 /. i) or ( i + 1 in dom b1 & F . (b1 /. i) = (L * (b2 /. i)) + (b2 /. (i + 1)) ) ) ) holds
ex J being non-empty FinSequence_of_Jordan_block of L,K st AutMt (F,b1,b2) = block_diagonal (J,(0. K))