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Easy · Market Microstructure · Quant Trader interview question · linear-algebra, covariance-matrix, positive-definite, correlation-matrix
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).