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 by (rough) units. Most code corresponds to a youtube video discussing it and the broader topics in linear algebra.

At the end of the day this is a place where I can put my notes/experiments for concepts/applications/tests involving numcerical 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

Unit 4 : Applications of Singular Values

• The Moore-Penrose Pseudo-Inverse

  • Video: https://youtu.be/5WHRLj77Tmw

• Numerical Methods for Determinants

  • Video: TBD

• Data and Image Compression with the SVD

  • Video: TBD