TL;DR
Non-zero vectors \( \mathbf{v} \) satisfying \( A\mathbf{v} = \lambda\mathbf{v} \). They define directions that are only scaled (not rotated) by the linear transformation A.
Eigenvectors
Non-zero vectors \( \mathbf{v} \) satisfying \( A\mathbf{v} = \lambda\mathbf{v} \). They define directions that are only scaled (not rotated) by the linear transformation A.
Why it matters for interviews
Eigenvectors of the covariance matrix are the principal components -- the uncorrelated risk factors. Understanding eigenvectors is essential for PCA-based factor models and portfolio construction.
Definition and Mathematical Foundation
Non-zero vectors \( \mathbf{v} \) satisfying \( A\mathbf{v} = \lambda\mathbf{v} \). They define directions that are only scaled (not rotated) by the linear transformation A.
Application in Quantitative Finance
Eigenvectors of the covariance matrix are the principal components -- the uncorrelated risk factors. Understanding eigenvectors is essential for PCA-based factor models and portfolio construction.
Related Terms
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