theorem Th15: :: MATRIX13:15

for n being Nat
for K being Field
for M being Matrix of n,K
for M1, M2 being upper_triangular Matrix of n,K st M = M1 * M2 holds
( M is upper_triangular Matrix of n,K & diagonal_of_Matrix M = mlt ((diagonal_of_Matrix M1),(diagonal_of_Matrix M2)) )