Linear Algebra: Applications in Statistics · Introduction

Introduction

What this guide covers

Introduction Introduction Geometry of multivariate analysis · Algebraic foundations

Overview

Topics covered

Introduction
Vector spaces and the geometry of multivariate data
Projection matrices and the centering operator
Quadratic forms and their statistical moments
The multivariate normal distribution
Linearity Property

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

X = \begin{bmatrix} 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{bmatrix} = \begin{bmatrix} \mathbf{x}_{1\cdot}^T \\ \mathbf{x}_{2\cdot}^T \\ \vdots \\ \mathbf{x}_{n\cdot}^T \end{bmatrix} = \begin{bmatrix} \mathbf{x}_{\cdot 1} & \mathbf{x}_{\cdot 2} & \cdots & \mathbf{x}_{\cdot p} \end{bmatrix}

View LaTeX source

X = \begin{bmatrix}
    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{bmatrix} = \begin{bmatrix}
    \mathbf{x}_{1\cdot}^T \\
    \mathbf{x}_{2\cdot}^T \\
    \vdots \\
    \mathbf{x}_{n\cdot}^T
    \end{bmatrix} = \begin{bmatrix}
    \mathbf{x}_{\cdot 1} & \mathbf{x}_{\cdot 2} & \cdots & \mathbf{x}_{\cdot p}
    \end{bmatrix}