Before Machine Learning Volume 1 - Linear Algebra for A.I

Chapter 5Break Them Down - Matrix Decomposition

We started simple, with a vector, and from that geometric idea we made our way through many linear algebra concepts. Some of them apply directly to real-world scenarios, like the dot product. Others are somewhat more abstract but still have great applicability to helping us deduce different concepts in linear algebra, like the eigenvectors. With the eigenvectors came a form of matrix decomposition, the eigendecomposition. We transformed a matrix into a product of three different matrices, namely two rotations and a scaling term. It is not a rule to decompose a matrix into three matrices. There are cases where we can decompose a matrix into a product of two others. However, in this book, we will ...