Exercise · ZW-CHOLESKY-FACTORIZATION-003 · ★☆☆ Basic
If \(L\) is the Cholesky factor, what does the equality \(A = LL^{T}\) express?
Choose one option.
Show answer
- D. That \(A\) decomposes as the product of \(L\) and its transpose
Explanation
The equality states that \(A\) is the product of \(L\) with its transpose. The other options describe relations that do not appear in the factorization.
Review the concept: Cholesky factorization
The Cholesky factorization decomposes a symmetric positive definite matrix \(A\) as \(A = LL^{T}\), where \(L\) is lower triangular with positive diagonal.
\[A = LL^{T}, \; l_{jj} = \sqrt{a_{jj} - \sum_{k
More practice problems: cholesky factorization
- ZW-CHOLESKY-FACTORIZATION-001 What property must a matrix A have to apply the Cholesky factorization?
- ZW-CHOLESKY-FACTORIZATION-002 What form does the factor L have in A = LL^T?
- ZW-CHOLESKY-FACTORIZATION-004 What is the element l_11 of the Cholesky factor when a_11=9?
- ZW-CHOLESKY-FACTORIZATION-005 What is the relation between Cholesky and LU for a symmetric positive definite matrix?
- ZW-CHOLESKY-FACTORIZATION-006 Compute l_11 and l_21 for A=[4 2; 2 5].
- ZW-CHOLESKY-FACTORIZATION-007 If a_22=10 and l_21=3, what is l_22?
- ZW-CHOLESKY-FACTORIZATION-008 For A=[9 3; 3 5], what is the factor L?
- ZW-CHOLESKY-FACTORIZATION-009 If L=[2 0; 1 2], what is the product LL^T?
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