I am still reading it.
Chapter One: makes the case for why we need multivariate analysis. Talks about MV representation, descriptive stats (mean, variance, corr, cov)provides an interesting intuition that corr is the normalized cov. Ath the end it provides a section on visualizing multivariate data which is pretty useless (See Maneesh Agrawala's slides for a more in dept overview)
Chapter Two: is an overview of matrix algebra and random vectors. Some of the basic operations that are going to be used is presented here. Among them is finding the projection of a vector onto another vector which is very useful. Definitions for orthogonal vectors and matrices are presented. A^-1 = A^T. Thing s like positive definiteness is defined. And a useful thing is the diagram on page 65 that starts us on learning about the spread of data that will be used in chapter 3 to set the stage for PCA.
Chapter 3: Talks about intuition and geometric interpretation of variance and SD and I very much enjoyed it. The connection between determinants of a matrix and the volume of its parallelogram is just amazingly mind blowing. The chapter is kind of important as it talks about equations for sample mean and variance. The math is just about the right amount and prepares you for later.
Chapter 4: is on Multivariate Normal and is kind of important.
Chapter 5, 6: Have not read
Chapter 7: Multivariate Linear Regression. Related to multivariate sentiment analysis
Chapter 8: is on PCA and is related to my research
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