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Exercise 2.7.34

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The product $L {(U^{T})}^{- 1}$ is lower triangular times lower triangular, so lower triangular. The transpose of $U^{T} DU$ is $U^{T} D^{T} U^{T} T = U^{T} DU$ again, so $U^{T} DU$ is symmetric. The factorization multiplies lower triangular by symmetric to get $LDU$ which is $A$ .

mathchakra

2022-01-16 12:45

Exercise 2.7.34

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