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Evolution of Linear Algebra: From Babylon to Modern Applications

Explore the fascinating history of linear algebra from Babylonian times to the contributions of pioneers like Hermann Grassmann, Johann Gauss, and Arthur Cayley. Learn about key discoveries, including Gaussian elimination and matrix theory, with practical applications in physics and mathematics.

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Evolution of Linear Algebra: From Babylon to Modern Applications

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  1. Numerical Linear Algebra By: Tiffany McKnight Robert Chirwa Alice Lin

  2. History of Linear Algebra • Babylon ~1900 BC • Had an advanced mathematical system • Base 60 • Developed tables to calculate formulas • Simple Linear equations • a x = b

  3. History continued • Father of Linear algebra • Hermann Grassmann • Showed how to apply vectors to important applications • Vector spaces • Forces (Physics)

  4. Hermann Grassman

  5. Grassmann’s Life • Born in 1809 • Died in 1877 • Studied 3 yrs in berlin • Never formally studied Mathematics • School teacher

  6. Grassmann’s Life • Wrote • Ausdehnunglsehre = Theory of Extension • Drew the attention of Mathematicians from around the world • 1842, 1860 • Theory of Tides • Textbooks • Translations for Encyclopedia Brittanica

  7. Hermann Grassmann • Proved integer’s properties • Proved Primary Decomposition Theorem • Took a century to for his works to be recognized • Had work stolen by Cauchy

  8. Johann Carl Friedrich Gauss

  9. Johann Gauss’s Life • Born 1777 • Died 1855 • Extremely good at Mathematics since an early age • Extensive Schooling • Many discoveries by the age of 19

  10. Johann Gauss’s Life • Became interested in Astronomy • Wanted to work on projects that were beneficial • Created Gaussian Elimination around 1800 • Created Gaussian Distribution Curve

  11. Arthur Cayley

  12. Arthur Cayley’s Life • Born 1821 • Died 1895 • Gifted at Mathematics at an early age • Became a Lawyer • Finally got an University post

  13. Arthur Cayley’s Life • Developed Theory of Algebraic Invariance • Applied to the study of Space-Time Continuem • Worked on Matrices • foundation for quantum mechanics • Suggested Special Types of Geometry

  14. Other Algorithms • Cholesky Factorization/Decomposition

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