Covariance Matrix

Creator
Creator
Seonglae Cho
Created
Created
2023 Mar 23 4:57
Editor
Edited
Edited
2024 Nov 18 12:9
Σ=(σX2ρσXσYρσXσYσY2)\Sigma = \begin{pmatrix} \sigma_X^2 & \rho \sigma_X \sigma_Y \\ \rho \sigma_X \sigma_Y & \sigma_Y^2 \end{pmatrix}
  • Each row and column represents the covariance, and the diagonal elements are the variances
  • ρ\rho is correlation coefficient
  • You can freely rearrange the indices in the covariance matrix
 
S=1NΣn(xnxˉ)T(xnxˉ)=1NXTXS = \frac{1}{N}\Sigma_n(x_n - \bar{x})^T(x_n - \bar{x}) = \frac{1}{N}X^TX

Positive
Definite matrix

Variance is always positive and then
Eigenvalue
is also all positive.
 
 
 
 
 
 

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