Suppose A ∈ R^n×n is nonsingular and admits a factorization A = LU with ones on the diagonal of L. Prove that such a decomposition is unique. Hint: consider two factorizations A = L1U1 = L2U2, isolate the L factors on one side of this equation, and reason about the structure of each side.

Suppose A ∈ R^n×n is nonsingular and admits a factorization A = LU with ones on the diagonal of L. Prove that such a decomposition is unique. Hint: consider two factorizations A = L1U1 = L2U2, isolate the L factors on one side of this equation, and reason about the structure of each side.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Suppose A ∈ R^n×n is nonsingular and admits a factorization A = LU
with ones on the diagonal of L. Prove that such a decomposition is unique. Hint: consider two
factorizations A = L1U1 = L2U2, isolate the L factors on one side of this equation, and reason
about the structure of each side.

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