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Hard · Linear Algebra & Machine Learning · Quant Trader interview question · linear-algebra, eigenvalues, gershgorin, risk-management
You are developing a risk model for a portfolio of correlated assets. The correlation matrix, $A$, is a key input. Due to data limitations and estimation errors, the correlation matrix might not be perfectly accurate, potentially affecting eigenvalue calculations used for risk assessment. Given the following matrix: $A = \begin{bmatrix} 5 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & -5 \end{bmatrix}$ Using Gershgorin's Circle Theorem, determine the tightest interval that is guaranteed to contain all real eig