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Difficulty: Medium
Category: Data Science
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Topics: linear-algebra, cholesky-decomposition, positive-definite, matrix-analysis
A market maker is constructing a covariance matrix for a basket of assets. The matrix, denoted as $A$, is used in pricing options and managing portfolio risk. For computational efficiency and stability, the market maker wants to perform a Cholesky decomposition, which decomposes the matrix $A$ into $L L^T$, where $L$ is a lower triangular matrix. What is the necessary and sufficient condition for the Cholesky decomposition of matrix $A$ to exist?
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