Summary
In this chapter, we covered intermediate linear algebra and its implementations in R. We started by introducing the matrix determinant, a widely used property in numerical analysis. We highlighted the intuition behind the matrix determinant and its connection to matrix rank.
We also covered additional properties, including matrix trace and norm. In particular, we introduced three popular norms: L 1-norm, L 2-norm, and L ∞-norm. We detailed their mathematical constructs and calculation process.
Next, we covered eigendecomposition, which leads to a set of eigenvalues and eigenvectors of a square matrix. We provided a step-by-step derivation and analysis of the core equation, as well as the approach to compute them.
Finally, we covered PCA, a popular technique that’s used for dimension reduction. Specifically, we highlighted its role in removing collinearity in the dataset and provided a few ways to compute and visualize PCA results.
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