Exercise · ZW-CHOLESKY-FACTORIZATION-009 · ★★☆ Intermediate
If \(L=\begin{pmatrix}2&0\\1&2\end{pmatrix}\), what is the product \(LL^{T}\)?
Choose one option.
Show answer
- B. \(\begin{pmatrix}4&2\\2&5\end{pmatrix}\)
Explanation
Multiplying, the (2,2) entry is \(1+4=5\) and the rest match \(A\). The option with 4 in position (2,2) omits the term \(1^{2}\).
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-003 If L is the Cholesky factor, what does the equality A = LL^T express?
- 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-008 ZW-CHOLESKY-FACTORIZATION-010 →