Gaussian Elimination over Z/3 
Gaussian Elimination over Z/3
by Robert Donley
Video Lecture 3 of 35
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Date Added: March 14, 2015

Lecture Description

Matrix Theory: Find all solutions to the system of linear equations over the finite field Z/3: x+ 2y = 1, 2x + y = 2.

Course Index

  1. Matrix Inverse over the Complex Numbers
  2. Cramer's Rule over the Complex Numbers
  3. Gaussian Elimination over Z/3
  4. Matrix Inverse over Z/7
  5. Cramer's Rule over Z/5
  6. Example of Skew-Symmetric Matrix
  7. Example of Simultaneous Diagonalization
  8. Positive Semi-Definite Matrix 1: Square Root
  9. Positive Semi-Definite Matrix 2: Spectral Theorem
  10. Positive Semi-Definite Matrix 3: Factorization of Invertible Matrices
  11. Cayley-Hamilton Theorem for 2x2 Matrices
  12. Inverse of a Matrix Using the Cayley-Hamilton Theorem
  13. Cayley-Hamilton Theorem: General Case
  14. Cayley-Hamilton Theorem: Example 1
  15. Cayley-Hamilton Theorem Example 2
  16. Example of Invariant Subspace
  17. Overview of Jordan Canonical Form
  18. Example of Jordan Canonical Form: 2x2 Matrix
  19. Example of Jordan Canonical Form: General Properties
  20. Example of Jordan Canonical Form: Real 4x4 Matrix with Basis 1
  21. Example of Jordan Canonical Form: Real 4x4 Matrix with Basis 2
  22. Commutant of Complex Matrix
  23. Example of Rational Canonical Form 1: Single Block
  24. Example of Rational Canonical Form 2: Several Blocks
  25. Example of Rational Canonical Form 3
  26. Exponential of 2x2 Matrix 1: Complex Case
  27. Exponential of 2x2 Matrix 2: Traceless Case
  28. Example of Group Action
  29. Example of Quaternions
  30. The Fibonacci Numbers Using Linear Algebra (HD Version)
  31. The Fibonacci Numbers Using Power Series
  32. Example of Group Automorphism 1 (Requires Linear Algebra)
  33. Example of Group Automorphism 2: G = Z/4 x Z/4 (Requires Linear Algebra)
  34. Group Theory: The Simple Group of Order 168 - Part 1
  35. Group Theory: The Simple Group of Order 168 - Part 2

Course Description

This set contains linear algebra over fields other than R and topics concerning matrices, such as canonical forms and groups.

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