Suppose I have a covariance matrix $\Sigma$, with eigenvalues $u_1,u_2,u_3$ and eigenvectors $v_1,v_2,v_3$. How can I use that information to generate a new covariance matrix $\Sigma_2$ with the same eigenvectors but with some new eigenvalues $\alpha u_1, u_2, u_3$?
2026-04-03 21:20:24.1775251224
Make a covariance matrix have a larger eigenvalue for one eigenvector
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