Gershgorin Circle Estimation - Quant Trader Interview Question
Difficulty: Hard
Category: Linear Algebra & Machine Learning
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Topics: linear-algebra, eigenvalues, gershgorin, risk-management
Problem Description
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
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