Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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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Step 1: Isolate L1 factor
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Step 2: Isolate L2 factor
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