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Eigenvalues, Eigenvectors, and Diagonalization with R

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Overview

This course introduces students to eigenvalues, eigenvectors, and matrix diagonalization. Focusing on matrix transformations, students will explore practical applications of these concepts using base R to solidify their understanding of advanced linear algebra principles.

Syllabus

Unit 1: Introduction to Eigenvalues

Calculating Eigenvalues and Eigenvectors in R
Exploring Matrix Impact on Eigenvalues and Eigenvectors
Debugging Eigenvalue Computation in R
Complete Eigenvalues and Eigenvectors Calculation in R
Calculating Eigenvalues and Eigenvectors from Scratch

Unit 2: Matrix Diagonalization in R

Matrix Diagonalization Using R
Matrix Diagonalization Practice with R
Matrix Diagonalization Debugging Task
Matrix Diagonalization in R
Matrix Diagonalization and Reconstruction Task

Unit 3: Matrix Powers with R

Matrix Power Calculation Using Eigen Decomposition in R
Matrix Power Computation Using Eigen Decomposition
Matrix Power Debugging Challenge
Complete Matrix Power Calculation Using Eigen Decomposition in R
Matrix Power Calculation Using Eigen Decomposition from Scratch

Unit 4: Singular Value Decomposition

Exploring Singular Value Decomposition with R
Exploring Singular Value Decomposition with Matrix Alterations
Fixing Singular Value Decomposition Code in R
Performing Singular Value Decomposition on a Matrix in R
Singular Value Decomposition from Scratch in R

Unit 5: Solving Linear Systems

Solving Linear Equations with R
Modifying Coefficient Matrix to Solve Systems of Equations in R
Identifying and Fixing Errors in R Code for Solving Systems of Equations
Solving Systems of Linear Equations in R
Solving Systems of Equations in R

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