By: Tim Bower

Mathematics for Cyber Systems Study Guide

This study guide is available from timbower.us.

This study guide is made available by the Creative Commons Attribution 3.0 United States License.

This Mathematics for Cyber Systems Study Guide provides notes and information for the Applied Mathematics for Cyber Systems (CYBR 280) course offered by K–State Salina, which is the campus of Kansas State University located in Salina, Kansas. Self study of the material in the Study Guide is welcome.

Contents:

• 1. Welcome to Data Analysis and Tools
  • 1.1. Introduction to the Course
  • 1.2. Weekly Schedule
• 2. Introduction to Linear Algebra
  • 2.1. Python for Linear Algebra Applications
  • 2.2. Working with Vectors
  • 2.3. Working with Matrices
  • 2.4. Geometric Transforms
  • 2.5. Systems of Linear Equations
  • 2.6. Elimination
  • 2.7. LU Decomposition
  • 2.8. Cholesky Decomposition for Positive Definite Systems
  • 2.9. Numerical Stability
  • 2.10. Orthogonal Matrix Decompositions
  • 2.11. Over-determined Systems and Vector Projections
  • 2.12. Under-determined Systems
• 3. Least Squares Regression
  • 3.1. Linear Regression
  • 3.2. Quadratic and Higher Order Regression
  • 3.3. Python’s Regression Functions
  • 3.4. Goodness of a Fit
  • 3.5. Generalized Least Squares Regression
  • 3.6. Fitting Exponential Data
• 4. Application of Eigenvalues and Eigenvectors
  • 4.1. Introduction to Eigenvalues and Eigenvectors
  • 4.2. Eigenvector Animation
  • 4.3. Finding Eigenvalues and Eigenvectors
  • 4.4. Properties of Eigenvalues and Eigenvectors
  • 4.5. Diagonalization and Powers of A
  • 4.6. Change of Basis and Difference Equations
• 5. Singular Value Decomposition (SVD)
  • 5.1. The Geometry of the SVD
  • 5.2. How SVD Changes Vectors
  • 5.3. Rank from the SVD
  • 5.4. Condition Number
  • 5.5. Fundamental Matrix Subspaces
  • 5.6. Dimensionality Reduction
  • 5.7. Other Applications of the SVD
• 6. Principal Component Analysis (PCA)
  • 6.1. PCA for Data Analysis
  • 6.2. PCA for Classification
  • 6.3. PCA for Recognition
• 7. Image Formation
  • 7.1. Cameras
  • 7.2. Perspective Projection Model
  • 7.3. Homography
  • 7.4. Stereo Cameras
  • 7.5. Active 3D Sensors
• 8. Orthogonal Matrix Factoring
  • 8.1. Matrix Factorizations
  • 8.2. Unitary Transformation Matrices
  • 8.3. QR Decomposition
  • 8.4. The Solution to the Eigenvalue Problem
  • 8.5. Calculating the SVD with Unitary Transformations
• 9. Appendix
  • 9.1. Norms
  • 9.2. Vector Spaces
  • 9.3. Finding Orthogonal Basis Vectors
  • 9.4. Linearly Independent Eigenvectors Theorem
  • 9.5. History of the Eigenvalue Problem
  • 9.6. All About the Number e
• 10. Bibliography
• 11. Homework
  • 11.1. Python Numpy and Vector Homework
  • 11.2. First Matrix Homework
  • 11.3. Systems of Equations Homework

Indices and tables

• Index

• Module Index

• Search Page