LU-Decomposition of a Matrix with Entries of Different Kinds (線型計算の標準算法と実現)

Abstract Let F ⊃ K be fields, and consider a matrix A over F whose entries not belonging to K are algebraically independent transcendentals over K . It is shown that if det A e K ∗ ( = K − {O}) , the matrix A , with suitable permutations of its rows and columns, is decomposed into LU -factors with the entries of the U -factor belonging to K .