[Solved] What is the result of applying Cholesky decomposition to a positive definite matrix A? — Ans: A lower triangular matrix L such that A = L L^T | SciPy

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What is the result of applying Cholesky decomposition to a positive definite matrix A?

AAn upper triangular matrix <code>U</code> such that <code>A = U U^T</code>

BA lower triangular matrix <code>L</code> such that <code>A = L L^T</code>

CA diagonal matrix containing eigenvalues of <code>A</code>

DA matrix of singular values of <code>A</code>

Step-by-Step Solution

Solution:

Step 1: Understand Cholesky decomposition
It decomposes a positive definite matrix A into L L^T, where L is lower triangular.
Step 2: Identify the output
The output is the lower triangular matrix L, not upper triangular or diagonal matrices.
Final Answer:
A lower triangular matrix L such that A = L L^T -> Option B
Quick Check:
Check if A = L L^T holds [OK]

Quick Trick: Cholesky gives lower triangular factorization [OK]

Common Mistakes:

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What is the result of applying Cholesky decomposition to a positive definite matrix A?