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Linear algebra for advanced studies
·
Module 7
Applications in Data Analysis
1
Least Squares for Overdetermined Systems
Formulate the least squares problem for overdetermined linear systems.
2
Solving Least Squares: Normal Equations & QR Decomposition
Solve the least squares problem using the normal equations or QR decomposition.
3
Pseudoinverse for Least Squares
Find the least squares solution using the pseudoinverse (derived from SVD).
4
PCA: Maximizing Variance
Describe the conceptual framework of Principal Component Analysis (PCA) as finding directions of maximum variance.
5
PCA and SVD: A Fundamental Relationship
Relate the principal components of a dataset to the singular vectors of the centered data matrix.
Previous module
Singular Value Decomposition (SVD)
Next module
Tensor Products for Composite Systems