theorem Th24: :: MATRIXJ1:24

for D being non empty set
for d being Element of D
for M1, M2 being Matrix of D
for M being Matrix of Sum (Len <*M1,M2*>), Sum (Width <*M1,M2*>),D holds
( M = block_diagonal (<*M1,M2*>,d) iff for i being Nat holds
( ( i in Seg (width M1) implies Col (M,i) = (Col (M1,i)) ^ ((len M2) |-> d) ) & ( i in Seg (width M2) implies Col (M,(i + (width M1))) = ((len M1) |-> d) ^ (Col (M2,i)) ) ) )