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