I am trying to work through the method described in this paper of calculating a normalcy index using principal component analysis. I understand steps 1-5, except for the equation for eigenvectors which is $\mathbf e_i = \sum_{j=1}^N \alpha_j^ix_j$ where $\alpha_j^i$ are "relative weights determined solely by the orthonormality constraint." The matrix containing $\mathbf x_j$ is a 10x8 matrix but the eigenvectors ($\mathbf e_i$) are from the covariance matrix which is 8x8 (I did that part in MATLAB). Because there is a difference in matrix dimensions I can't divide $\mathbf e_i$ by $\mathbf x_j$ to find $\mathbf \alpha_j^i$. I need $\mathbf \alpha_j^i$ to complete the next steps (as far as I can tell) including mutiplying it by another 10x8 matrix $\mathbf z_j$. Please help me understand how I'm supposed to calculate $\mathbf \alpha_j^i$
2026-03-28 10:03:43.1774692223
How to calculate reletive weights (alpha) in Principal Component Analysis
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