theorem Th25: :: MATRIXJ2:25

for K being Field
for V1 being finite-dimensional VectSp of K
for b1 being OrdBasis of V1
for J being FinSequence_of_Jordan_block of 0. K,K
for M being Matrix of len b1, len b1,K st M = block_diagonal (J,(0. K)) holds
for m being Nat st ( for i being Nat st i in dom J holds
len (J . i) <= m ) holds
(Mx2Tran (M,b1,b1)) |^ m = ZeroMap (V1,V1)