Statistical Modeling & Regression · Multivariate Analysis

Multivariate analysis: Foundations of matrix algebra and multivariate data

Public introduction · full guide in Eikos

Introduction

What this guide covers

A deep analytical dive into applied linear algebra and formal modeling of simultaneous random variables. An advanced level text for researchers and data scientists.

Overview

Topics covered

  • Introduction
  • Matrix Algebra and Multivariate Data
  • Introduction to Multivariate Analysis and Multivariate Data
  • The Formal Structure of the Data Matrix
  • Geometry of Multivariate Space: Dual Representation
  • Multivariate Sample Statistics and the Centering Operator

Related concepts

Main connections

  • Linear algebra & matrices
  • Maximum likelihood estimation
  • Variance & standard deviation
  • Calculus & differentiation
  • Normal (Gaussian) distribution
  • Mean & expected value

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

𝐗=(x11x12⋯x1px21x22⋯x2p⋮⋮⋱⋮xn1xn2⋯xnp)
View LaTeX source\mathbf{X} = \begin{pmatrix} x_{11} & x_{12} & \cdots & x_{1p} \\ x_{21} & x_{22} & \cdots & x_{2p} \\ \vdots & \vdots & \ddots & \vdots \\ x_{n1} & x_{n2} & \cdots & x_{np} \end{pmatrix}