Covariance Matrix Validity - Quant Trader Interview Question
Difficulty: Easy
Category: Market Microstructure
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Topics: linear-algebra, covariance-matrix, positive-definite, correlation-matrix
Problem Description
You are given a $3 \times 3$ matrix representing a candidate for a correlation matrix.
$$ \begin{pmatrix} 1 & 0.9 & 0.9 \\ 0.9 & 1 & 0.9 \\ 0.9 & 0.9 & 1 \end{pmatrix} $$
Determine whether this matrix can be a valid correlation matrix. A correlation matrix must be symmetric, have 1s on the diagonal, and be positive semi-definite (PSD).
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