Computational and Numerical Linear Algebra

This repository contains example code and Python Jupyter notebooks on various topics related to computational and numerical linear algebra. The contents are divided into three units. Each bit of code corresponds to a youtube discussing it and the broader topics in linear algebra.

Unit 1: Matrix Decompositions

• Introduction to Linear Systems
  • Video: https://youtu.be/8E2858kWVEw
• Triangular Matrices
  • Video: https://youtu.be/C5yRi7EbKXM
• Forward and Backwards Substitution
  • Video: https://youtu.be/hnBpWrE7L4k
• Gaussian Elimination
  • Video: https://youtu.be/59TAcVWZ0LY
• LU Decomposition
  • Video: https://youtu.be/joDOPaHVDnI
• LDV Decomposition
  • Video:https://youtu.be/stCSZ9KY6eQ
• Cholesky Decomposition
  • Video: https://youtu.be/o5V69gQcLt0
• LDL Transpose Decomposition
  • Video:https://youtu.be/Vg34n4k5Ar4

Unit 2: Non-Square Matrices and Basic Data Fitting

• Non-Square Linear Systems
  • Video: https://youtu.be/aoG6Ydxh_Fc
• The Method of Least Squares
  • Video: https://youtu.be/KP3OvpPXtys
• Line Fitting
  • Video: https://youtu.be/AMkUVQAw6MU
• Polynomial Fitting
  • Video: https://youtu.be/TZAtc06QkmM
• Exponent Fitting
  • Video: https://youtu.be/aObGTXd6Oug

Unit 3: Orthogonal and Orthonormal Matrices, Eigenvalues, and Singular Values

• Orthogonal and Orthonormal Sets of Vectors

  • Video: https://youtu.be/pi70r8xBvnw

• The Gram-Schmidt Process

  • Video: https://youtu.be/SChiY-2MiWo

• Benchmarking Orthonormal Systems

  • Video: https://youtu.be/3o4XWIJTNxI

• The QR Matrix Decomposition

  • Video: https://youtu.be/kyG8YMIfNA0

• Numerical Methods for Computing Eigenvalues

  • Video: https://youtu.be/5sFQdEl9MTU

• Singular Value Decomposition

  • Video: https://youtu.be/O9loiz1AcZg