Linear Algebra

Last updated Sep 3, 2022 Edit Source

Mathematical discipline that deals with vectors and matrices and, more generally, with vector spaces and linear transformations

• https://en.wikipedia.org/wiki/Linear_algebra
• https://www.britannica.com/science/linear-algebra
• The Matrix Cookbook (Brandt 2012)
• Stanford, Linear algebra refresher
• Stanford CS229, algebra and calculus refresher:
  • https://github.com/afshinea/stanford-cs-229-machine-learning/blob/master/en/refresher-algebra-calculus.pdf
  • http://cs229.stanford.edu/section/cs229-linalg.pdf
• http://people.duke.edu/~ccc14/sta-663/LinearAlgebraReview.html
• https://www.khanacademy.org/math/linear-algebra
• http://nbviewer.jupyter.org/github/relopezbriega/relopezbriega.github.io/blob/master/downloads/LinearAlgebraPython.ipynb

• See AI/Unsupervised learning/Dimensionality reduction and low rank modeling
• See AI/Math and Statistics/SVD
• https://en.wikipedia.org/wiki/Matrix_decomposition
• http://people.duke.edu/~ccc14/sta-663/LinearAlgebraMatrixDecompWithSolutions.html
• http://hameddaily.blogspot.be/2016/12/simple-matrix-factorization-with.html
• https://sites.google.com/site/igorcarron2/matrixfactorizations
• http://blog.ethanrosenthal.com/2017/06/20/matrix-factorization-in-pytorch/
• https://tryolabs.com/blog/introduction-to-recommender-systems/
• Alternating Least-squares
  • Fast Python Collaborative Filtering for Implicit Datasets
  • Recommender system using matrix factorization (SVD, ALS)
• Eigen decomposition:
  • https://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix
  • http://setosa.io/ev/eigenvectors-and-eigenvalues/
• LU decomposition
• QR decomposition

• #CODE Tensorly
  • http://tensorly.org
  • TensorLy is a Python library that aims at making tensor learning simple and accessible. It allows to easily perform tensor decomposition, tensor learning and tensor algebra. Its backend system allows to seamlessly perform computation with NumPy, PyTorch, JAX, MXNet, TensorFlow or CuPy, and run methods at scale on CPU or GPU
  • https://github.com/JeanKossaifi/tensorly-notebooks/
  • http://tensorly.org/stable/modules/api.html#module-tensorly.decomposition
• #CODE Eigen - Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms
• #CODE https://github.com/rballester/tntorch

• #BOOK Templates for the Solution of Algebraic Eigenvalue Problems (Bai, Demmel 2000)
• #BOOK High Dimensional Data Analysis 2020 (HDA2020)

• #PAPER tntorch: Tensor Network Learning with PyTorch (Usvyatsov 2022)
  • https://www.marktechpost.com/2022/06/30/eth-zurich-ai-researchers-introduce-tntorch-a-pytorch-powered-tensor-learning-python-library-that-supports-multiple-decompositions-under-a-unified-interface/