Week 8
Dotted with an (matr)I(x): Interactions between linear transformations and inner products, symmetric matrices, Singular Value Decomposition
8.1: Inner products and linear transformations, self-adjoint transformations and symmetric matrices
Harnessing previous knowledge, we can analyze how the idea of inner products, symmetry, and linear transformations come together.
These notes will explore how dot products relate to linear transformations, defining self-adjoint and orthogonal transformations. Further, the properties of a transformation when the matrix is symmetric, a subset of self-adjoint transformations.
Singular Value Decomposition (SVD) and its statistical application, Principal Component Analysis (PCA), are powerful techniques in linear algebra and data analysis.
In these notes, you’ll explore Singular Value Decomposition, a special type of matrix factorization that can be done for square and non-square matrices.
8.2: Singular value decomposition and principal component analysis
Recitation Slides
Attend recitation! But in case you were staying up late the night before or you’re looking to last-minute study cram, here are Week 8 recitation slides and solutions!
Ryann Joseph 