- Home
- TGTS
- Courses
- Student Recognitions
- Student Projects
- Papers to View/Download
- Slides from Recent Talks
- Curriculum
- About the Professor
MATH 422 - Linear Algebra 2
Course Information
Solutions to Problem Sets and Final Exam
- Problem Set #1 Solutions
- Problem Set #2 Solutions
- Problem Set #3 Solutions
- Article: Sums of Powers by Matrix Methods by Dan Kalman
- Take-home Final Exam
Courseware
- Elementary linear operators on the plane (Mathematica notebook)
- Similitudes on the plane (Mathematica notebook)
- Rotations in the plane (Mathematica notebook)
- 3D computer graphics (Mathematica notebook)
- Rotating 3D cube (Mathematica notebook)
- Rotate about the y-axis and project to the yz-plane (Mathematica notebook)
- Rotating 4D Hypercube (Mathematica notebook)
- Schur triangularization Example (Mathematica notebook)
- Winfeed fractal software (Peanut software by Rick Parris)
- Anton's fractal 3c, p. 702
Handouts
- Matrix representations of a linear map
- Dimension, rank and nullity
- Rotations in the plane as a product of elementary operations
- Change of coordinates, reflections in the plane and rotations in space
- Real inner product spaces and orthogonal transformations
- Simpson's Rule
- Orthogonal diagonalization
- The Fibonacci sequence, the golden ratio and matrix powers
- Quadratic forms
- The 2nd derivative test for functions of two variables
- Length contraction and time dilation in space-time
- Reduction to Hessenberg form (Algorithm 1)
- Householder reduction to Hessenberg form (Algorithm 2)
- The Cayley-Hamilton Theorem: Steps in the proof
- Generalized eigenvectors and systems of differential equations
- Schur's Triangularization Theorem
- Another proof of the Cayley-Hamiliton Theorem
- The Range-Nullspace decomposition of Cn
- The Core-Nilpotent decomposition of singular matrices
- Jordan canonical form of a nilpotent matrix
- Jordan Form of a general matrix
- Solutions to Exercises on general Jordan Form
- Powers of Jordan blocks
- Solution to Exercise 3 in Powers of Jordan blocks