References#

Historical Development#

History of algebra - Wikipedia, accessed August 31, 2025
https://en.wikipedia.org/wiki/History_of_algebra

History of Linear Algebra - University of Utah, accessed August 31, 2025
https://www.math.utah.edu/~gustafso/s2012/2270/web-projects/christensen-HistoryLinearAlgebra.pdf

Matrices and determinants - MacTutor History of Mathematics, accessed August 31, 2025
https://mathshistory.st-andrews.ac.uk/HistTopics/Matrices_and_determinants/

Linear concepts - EBSCO Research Starters, accessed August 31, 2025
https://www.ebsco.com/research-starters/science/linear-concepts

Ancient Mathematics#

An Overview of Babylonian Mathematics - University of Kentucky, accessed August 31, 2025
https://www.ms.uky.edu/~droyster/courses/fall06/PDFs/AppendixA.pdf

Babylonian mathematics - MacTutor - University of St Andrews, accessed August 31, 2025
https://mathshistory.st-andrews.ac.uk/HistTopics/Babylonian_mathematics/

A Brief Study of Some Aspects of Babylonian Mathematics - University of Hawaii, accessed August 31, 2025
https://www.math.hawaii.edu/~mchyba/documents/syllabus/Math499/Babylonians/Babylonian.pdf

Chinese Mathematical Traditions#

Early History of Linear Algebra - Roger Hart, accessed August 31, 2025
http://rhart.org/algebra/

The Chinese Roots of Linear Algebra - Jesus College in the University of Cambridge, accessed August 31, 2025
https://www.jesus.cam.ac.uk/articles/chinese-roots-linear-algebra

A Classic from China: The Nine Chapters - Harvard Mathematics, accessed August 31, 2025
https://people.math.harvard.edu/~knill/teaching/math22a2018/exhibits/gaussjordan/SchwarzNineChapters.pdf

The Nine Chapters on the Mathematical Procedures - Britannica, accessed August 31, 2025
https://www.britannica.com/topic/The-Nine-Chapters-on-the-Mathematical-Procedures

Illustrating The Nine Chapters on the Mathematical Art: Their Use in a College Mathematics History Classroom - MAA, accessed August 31, 2025
https://old.maa.org/press/periodicals/convergence/illustrating-the-nine-chapters-on-the-mathematical-art-their-use-in-a-college-mathematics-history-1

Jiu Zhang Suan Shu and the Gauss Algorithm for Linear Equations - RIMS, Kyoto University, accessed August 31, 2025
http://www.kurims.kyoto-u.ac.jp/EMIS/journals/DMJDMV/vol-ismp/10_yuan-ya-xiang.pdf

The Nine Chapters on the Mathematical Art - Fiveable Study Guide, accessed August 31, 2025
https://library.fiveable.me/history-of-mathematics/unit-6/chapters-mathematical-art/study-guide/Aybg4BbsWzGPTG7i

The Chinese Roots of Linear Algebra - JHU Press, accessed August 31, 2025
https://www.press.jhu.edu/books/title/10232/chinese-roots-linear-algebra

Core Linear Algebra Development#

Linear algebra - Wikipedia, accessed August 31, 2025
https://en.wikipedia.org/wiki/Linear_algebra

A Brief History of Linear Algebra and Matrix Theory - Convex Optimization, accessed August 31, 2025
https://convexoptimization.com/TOOLS/Vitulli.pdf

The Evolution of Gaussian-Type Elimination - Loyola Marymount University, accessed August 31, 2025
https://digitalcommons.lmu.edu/cgi/viewcontent.cgi?filename=0&article=1191&context=honors-research-and-exhibition&type=additional

The Chinese Roots of Linear Algebra - Mathematical Association of America, accessed August 31, 2025
https://old.maa.org/press/maa-reviews/the-chinese-roots-of-linear-algebra

Gaussian Elimination#

Gaussian elimination - EBSCO Research Starters, accessed August 31, 2025
https://www.ebsco.com/research-starters/history/gaussian-elimination

Gaussian elimination - Wikipedia, accessed August 31, 2025
https://en.wikipedia.org/wiki/Gaussian_elimination

Gaussian Elimination - Numerical Analysis Lecture Notes - University of Minnesota, accessed August 31, 2025
https://www-users.cse.umn.edu/~olver/num_/lng.pdf

Gaussian Elimination: A Method to Solve Systems of Equations - DataCamp, accessed August 31, 2025
https://www.datacamp.com/tutorial/gaussian-elimination

Key Historical Figures#

The Secret History of Mathematicians - American Scientist, accessed August 31, 2025
https://www.americanscientist.org/article/the-secret-history-of-mathematicians

James Joseph Sylvester - Britannica, accessed August 31, 2025
https://www.britannica.com/biography/James-Joseph-Sylvester

Matrices and Determinants - Scribd, accessed August 31, 2025
https://www.scribd.com/document/712558805/2-Matrices-and-Determinants

Where would you use matrix algebra? - Math Blog, accessed August 31, 2025
https://mathsmartinthomas.wordpress.com/2015/12/06/where-would-you-use-matrix-algebra/

Hermann Grassmann and Vector Spaces#

Hermann Grassmann (1809 - 1877) - Biography - MacTutor History, accessed August 31, 2025
https://mathshistory.st-andrews.ac.uk/Biographies/Grassmann/

The Historical Movement of the Contributions of Grassmann's Extension Theory to Linear Algebra - Academic Journal, accessed August 31, 2025
http://educa.fcc.org.br/pdf/ob/v8/en_2526-7647-ob-8-e2024-33.pdf

The Extension Theory of Hermann Grassmann and the Creation of Vector Algebra - CORE, accessed August 31, 2025
https://core.ac.uk/download/pdf/231908059.pdf

Abstract linear spaces - MacTutor History of Mathematics, accessed August 31, 2025
https://mathshistory.st-andrews.ac.uk/HistTopics/Abstract_linear_spaces/

Hermann Grassmann - Wikipedia, accessed August 31, 2025
https://en.wikipedia.org/wiki/Hermann_Grassmann

Vector space - EBSCO Research Starters, accessed August 31, 2025
https://www.ebsco.com/research-starters/physics/vector-space

Abstract Vector Spaces and Concrete Examples - Oklahoma State University, accessed August 31, 2025
https://math.okstate.edu/people/binegar/3013-S99/3013-l12.pdf

Abstract vector spaces - 3Blue1Brown, accessed August 31, 2025
https://www.3blue1brown.com/lessons/abstract-vector-spaces

Physics Applications#

Mathematics of general relativity - Wikipedia, accessed August 31, 2025
https://en.wikipedia.org/wiki/Mathematics_of_general_relativity

How is linear algebra used in general relativity? - Reddit Discussion, accessed August 31, 2025
https://www.reddit.com/r/AskPhysics/comments/t2bbc3/how_is_linear_algebra_used_in_general_relativity/

Linear algebra basics - Oxford University Physics, accessed August 31, 2025
https://users.physics.ox.ac.uk/~lvovsky/quantumbook/app-a.pdf

Linear Algebra - University of Virginia Physics, accessed August 31, 2025
http://galileo.phys.virginia.edu/classes/751.mf1i.fall02/751LinearAlgebra.htm

Linear Algebra and Quantum Mechanics - Nicholas Rui Blog, accessed August 31, 2025
https://nicholasrui.com/2018/05/14/linear-algebra-and-quantum-mechanics/

Linear algebra for quantum mechanics help - Reddit Discussion, accessed August 31, 2025
https://www.reddit.com/r/AskPhysics/comments/ajrjzc/in_undergraduate_quantum_mechanics_havent_taken/

Computer Graphics Applications#

How Linear Algebra Powers Animation and 3D Graphics - Understand The Math, accessed August 31, 2025
https://www.understandthemath.com/blog/linear-algebra-in-animation

Mathematics for Computer Graphics - Georgia Tech, accessed August 31, 2025
https://faculty.cc.gatech.edu/~turk/math_gr.html

Computer Graphics - Linear Algebra - Brown University, accessed August 31, 2025
https://www.cfm.brown.edu/people/dobrush/cs52/Mathematica/Part7/graphics.html

Computer Graphics — Linear Algebra, Geometry, and Computation - Boston University, accessed August 31, 2025
https://www.cs.bu.edu/fac/snyder/cs132-book/L13ComputerGraphics-Spring2021.html

Data Science and Machine Learning#

Linear Algebra Required for Data Science - GeeksforGeeks, accessed August 31, 2025
https://www.geeksforgeeks.org/data-science/linear-algebra-required-for-data-science/

Linear Algebra Concepts Every Data Scientist Should Know - Medium, accessed August 31, 2025
https://medium.com/bitgrit-data-science-publication/linear-algebra-concepts-every-data-scientist-should-know-18b00bd453dd

Practical Guide to Linear Algebra in Data Science and AI - freeCodeCamp, accessed August 31, 2025
https://www.freecodecamp.org/news/linear-algebra-roadmap/

Linear Algebra for Machine Learning and Data Science - Coursera, accessed August 31, 2025
https://www.coursera.org/learn/machine-learning-linear-algebra

Network Analysis#

PageRank - Wikipedia, accessed August 31, 2025
https://en.wikipedia.org/wiki/PageRank

A Friendly Introduction to the PageRank Algorithm - Medium, accessed August 31, 2025
https://churchill-aloha.medium.com/pagerank-algorithm-explanation-code-2fb6c0389bed