Elsevier

Linear Algebra and its Applications

Volume 49, February 1983, Pages 275-283
Linear Algebra and its Applications

LU-decomposition of a matrix with entries of different kinds

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Abstract

Let FK 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 ε 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.

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