The Grid That Holds the Unknowns
In short: A method for solving many linear equations at once has a debated history in China and Europe and was later unified by matrix notation; matrices now also carry out linear transformations and support AI models, image processing and data compression.
A 1:31 short film in the series “From Fingers to Qubits”, narrated by intellect_voice_01.
Sources used in this film: University of Oxford, Department for Continuing Education (Oxford Lifelong Learning), “Linear Algebra: Introduction - Oxford Lifelong Learning”; The Open University (OpenLearn), “Introduction to linear equations and matrices”; Springer Nature (Springer, book chapter; the page does not name the author, though the notes cite Hart's earlier work), “Ancient Chinese Origins of Modern Western Science; or, The Early History of Linear Algebra”; arXiv (ar5iv HTML rendering of Joseph F. Grcar, "How Ordinary Elimination Became Gaussian Elimination"; the page asks readers to cite the corrected, published article), “How Ordinary Elimination Became Gaussian Elimination”; arXiv (Cornell University preprint server); preprint submitted by Emilien Dupont, “Improving the matrix multiplication exponent with modern optimization and AlphaEvolve”; Ars Technica, “Matrix multiplication advancement could lead to faster, more efficient AI models”.
Sources used in this film
- University of Oxford, Department for Continuing Education (Oxford Lifelong Learning) — Linear Algebra: Introduction - Oxford Lifelong Learning · View →
- The Open University (OpenLearn) — Introduction to linear equations and matrices · View →
- Springer Nature (Springer, book chapter; the page does not name the author, though the notes cite Hart's earlier work) — Ancient Chinese Origins of Modern Western Science; or, The Early History of Linear Algebra · View →
- arXiv (ar5iv HTML rendering of Joseph F. Grcar, "How Ordinary Elimination Became Gaussian Elimination"; the page asks readers to cite the corrected, published article) — How Ordinary Elimination Became Gaussian Elimination · View →
- arXiv (Cornell University preprint server); preprint submitted by Emilien Dupont — Improving the matrix multiplication exponent with modern optimization and AlphaEvolve · View →
- Ars Technica — Matrix multiplication advancement could lead to faster, more efficient AI models · View →
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Sources
- Summary by Intellect · source: University of Oxford, Department for Continuing Education (Oxford Lifelong Learning): Linear Algebra: Introduction - Oxford Lifelong Learning
- Also: The Open University (OpenLearn): Introduction to linear equations and matrices
- Also: Springer Nature (Springer, book chapter; the page does not name the author, though the notes cite Hart's earlier work): Ancient Chinese Origins of Modern Western Science; or, The Early History of Linear Algebra
- Also: arXiv (ar5iv HTML rendering of Joseph F. Grcar, "How Ordinary Elimination Became Gaussian Elimination"; the page asks re: How Ordinary Elimination Became Gaussian Elimination
- Also: arXiv (Cornell University preprint server); preprint submitted by Emilien Dupont: Improving the matrix multiplication exponent with modern optimization and AlphaEvolve
- Also: Ars Technica: Matrix multiplication advancement could lead to faster, more efficient AI models
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