Matrix Rank Inequality - Quant Trader Interview Question
Difficulty: Medium
Category: Probability & Statistics
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Topics: linear-algebra, rank, matrix, inequality
Problem Description
You are developing a high-frequency trading strategy that relies on dimensionality reduction techniques applied to large covariance matrices. Let $A$ be an $m \times n$ matrix representing feature loadings and $B$ be an $n \times p$ matrix representing portfolio weights. You are optimizing your algorithm and need to understand how the rank of the product $AB$ relates to the ranks of $A$ and $B$. Which of the following statements is ALWAYS true?
Context: The rank of a matrix reflects the number o
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