theorem :: MATRIX13:98

for K being Field
for M being Matrix of K holds
( the_rank_of M = 1 iff ex i being Nat st
( i in Seg (len M) & ex j being Nat st
( j in Seg (width M) & M * (i,j) <> 0. K ) & ( for k being Nat st k in Seg (len M) holds
ex a being Element of K st Line (M,k) = a * (Line (M,i)) ) ) )