{"id":20611934,"url":"https://github.com/particle1331/computational-linear-algebra","last_synced_at":"2026-03-06T14:32:01.046Z","repository":{"id":65468882,"uuid":"331876582","full_name":"particle1331/computational-linear-algebra","owner":"particle1331","description":"Rapidly develops the SVD and uses it for everything.","archived":false,"fork":false,"pushed_at":"2023-01-25T13:25:46.000Z","size":47090,"stargazers_count":4,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-10-11T11:16:04.821Z","etag":null,"topics":["a","linear-algebra","loss-surface","math","mathematics","matrix","moore-penrose-pseudoinverse","proof","svd"],"latest_commit_sha":null,"homepage":"","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/particle1331.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null}},"created_at":"2021-01-22T07:58:11.000Z","updated_at":"2024-08-07T03:36:13.000Z","dependencies_parsed_at":"2023-02-14T01:31:53.036Z","dependency_job_id":null,"html_url":"https://github.com/particle1331/computational-linear-algebra","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/particle1331/computational-linear-algebra","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/particle1331%2Fcomputational-linear-algebra","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/particle1331%2Fcomputational-linear-algebra/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/particle1331%2Fcomputational-linear-algebra/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/particle1331%2Fcomputational-linear-algebra/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/particle1331","download_url":"https://codeload.github.com/particle1331/computational-linear-algebra/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/particle1331%2Fcomputational-linear-algebra/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":30180672,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-03-06T12:39:21.703Z","status":"ssl_error","status_checked_at":"2026-03-06T12:36:09.819Z","response_time":250,"last_error":"SSL_connect returned=1 errno=0 peeraddr=140.82.121.5:443 state=error: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["a","linear-algebra","loss-surface","math","mathematics","matrix","moore-penrose-pseudoinverse","proof","svd"],"created_at":"2024-11-16T10:22:38.401Z","updated_at":"2026-03-06T14:32:01.008Z","avatar_url":"https://github.com/particle1331.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Computational Linear Algebra\n\n\nNotes and code experiments for linear algebra in code. The idea is to construct the SVD as soon as possible, then use it for everything else \u0026mdash; from characterizing invertibility, to parametrizing the loss surface of a linear regression model. Some of the interesting stuff that are covered:\n  * Proof of the real spectral theorem, and a code demo\n  * Proof of the singular value decomposition (SVD)\n  * An extensive discussion of the Moore-Penrose pseudoinverse\n  * Stability of the Gram-Schmidt algorithm\n  * Characterizing the loss surface of a linear regression problem\n  * Characterizing quadratic forms using the principal axes theorem\n\n\u003cbr\u003e\n\n\u003cp align=\"center\"\u003e\n    \u003cimg src='img/kde-decomp.png'\u003e\n    \u003cbr\u003e\n    \u003cb\u003eFigure.\u003c/b\u003e SVD of a sum of Gaussians. Only the first few vectors are meaningful, the rest model noise. \n\u003c/p\u003e\n\n\u003cbr\u003e\n\n\u003cp align=\"center\"\u003e\n    \u003cimg src='img/18_normalized_indefiniteQF.png'\u003e\n    \u003cbr\u003e\n    \u003cb\u003eFigure.\u003c/b\u003e Energy surface of an indefinite matrix. It has a negative minimum and a positive maximum.\n\u003c/p\u003e\n\n\u003cbr\u003e\n\n## Contents\n\n\n1. [Vectors and matrices](https://github.com/particle1331/computational-linear-algebra/blob/master/chapters/01-vectors.ipynb)\n2. [Singular value decomposition](https://github.com/particle1331/computational-linear-algebra/blob/master/chapters/02-svd.ipynb)\n3. [Matrix multiplication and norms](https://github.com/particle1331/computational-linear-algebra/blob/master/chapters/03-norms.ipynb)\n4. [Rank and dimension](https://github.com/particle1331/computational-linear-algebra/blob/master/chapters/04-rank.ipynb)\n5. [Four fundamental subspaces](https://github.com/particle1331/computational-linear-algebra/blob/master/chapters/05-four-subspaces.ipynb)\n6. [Determinant](https://github.com/particle1331/computational-linear-algebra/blob/master/chapters/06-det.ipynb)\n7. [Matrix inverse and pseudoinverse](https://github.com/particle1331/computational-linear-algebra/blob/master/chapters/07-inverse.ipynb)\n8. [Projection and orthogonalization](https://github.com/particle1331/computational-linear-algebra/blob/master/chapters/08-projection.ipynb)\n9. [Least squares for model fitting](https://github.com/particle1331/computational-linear-algebra/blob/master/chapters/09-least-squares.ipynb)\n10. [Eigendecomposition](https://github.com/particle1331/computational-linear-algebra/blob/master/chapters/10-eigendecomp.ipynb)\n11. [Quadratic form and definiteness](https://github.com/particle1331/computational-linear-algebra/blob/master/chapters/11-quadratic.ipynb)\n\n\u003cbr\u003e\n\n## Quick links\n\n* [Proofs involving the Moore-Penrose pseudoinverse](https://en.wikipedia.org/wiki/Proofs_involving_the_Moore%E2%80%93Penrose_inverse)\n* [KaTeX Supported Functions](https://katex.org/docs/supported.html)\n\n\n\u003cbr\u003e\n\n## References\n* [Mike X Cohen.](http://mikexcohen.com/) [*Complete linear algebra: theory and implementation in code*. Udemy. (2021)](https://www.udemy.com/course/linear-algebra-theory-and-implementation/)\n* [Sheldon Axler. *Down With Determinants!* The American Monthly. (1996)](https://www.maa.org/sites/default/files/pdf/awards/Axler-Ford-1996.pdf)\n* [Leslie Hogben (editor). *Handbook of Linear Algebra*. CRC Press. (2014)](https://www.oreilly.com/library/view/handbook-of-linear/9781466507296/)\n* [Cleve Moler. *Numerical Computing with MATLAB*. The MathWorks / SIAM. (2013)](https://www.mathworks.com/moler/index_ncm.html)\n* [Peter Olver and Chehzrad Shakiban. *Applied Linear Algebra*. UTM Springer. (2018)](https://www-users.math.umn.edu/~olver/books.html)\n* [Petersen \u0026 Pedersen. *The Matrix Cookbook*. v. Nov. 15, 2012. (2012)](https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf)\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fparticle1331%2Fcomputational-linear-algebra","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fparticle1331%2Fcomputational-linear-algebra","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fparticle1331%2Fcomputational-linear-algebra/lists"}