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Spectral Decomposition of Symmetric Matrices

Medium · Linear Algebra & Machine Learning · Quant Trader interview question · linear-algebra, spectral-theorem, symmetric-matrix, eigenvalues, eigenvectors, PCA

Suppose you are building a statistical arbitrage model that relies on principal component analysis (PCA) of a covariance matrix estimated from historical stock returns. The covariance matrix, $A$, is a real symmetric matrix. Which of the following statements correctly expresses the Spectral Theorem for real symmetric matrices?