Introduction

Gershgorin Circle Theorem

Independent Research Project

Introduction

One piece of helpful information to gather from any matrix is the exact or estimated value of the matrix’s eigenvalues. This paper provides some background information, properties, examples, and even a proof of one method utilized to find eigenvalues: The Gershgorin Circle Theorem. This method provides one way of estimating numerically and graphically where the eigenvalues of any matrix are located on the complex plane, ℂ.

My Role

Gather background information about Linear Algebra, including:
- Definition, characteristics, and applications of eigenvalues and eigenvectors
- Methods of finding eigenvalues, including multiple methods of solving characteristic equations
- Definition, proof, properties, and applications of the Gershgorin Circle Theorem
Clearly explain a proof of the Gershgorin Circle Theorem
Write code to calculate the eigenvalues and plot the Gershgorin Domain of example matrices
Produce research paper through writing and figure implementation

Technologies and Skills

Matlab
- Construct matrices and calculate eigenvalues
Mathematica
- Plot points and regions onto complex plane
Microsoft PowerPoint
Microsoft Word ( + importing LaTeX syntax)
Google Docs
Google Drive
Google Slides

Zoom (remote communication)
Mathematical Knowledge In:
- Numerical Analysis
- Linear Algebra
- Calculus
- Statistics
- Complex Analysis
- Numerical Optimization