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Numerical Linear Algebra

Numerical Linear Algebra. By: Tiffany McKnight Robert Chirwa Alice Lin. 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. History continued. Father of Linear algebra

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Numerical Linear Algebra

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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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