Notes on Linear Algebra Done Right by Axler
Change of Basis The major oversight of the book was what I thought a lack of focus on change of basis. This is the best way to understand matrix similarity in general and what PCA, SVD, and Product Quantization[https://www.pinecone.io/learn/series/faiss/product-quantization/] do in particular. I’ll go over the idea of basis in the abstract and then give a concrete example. Basis to Representation in the Abstract Not all vector spaces represent numbers along a set of dimensions, nor operators are represent coefficient multiplication on the underlying variables....