Linear Algebra for Data Science: A Textbook Overview, Study notes of Linear Algebra

Download Linear Algebra for Data Science: A Textbook Overview and more Study notes Linear Algebra in PDF only on Docsity!

L I N E A R A L G E B R A

An Introduction to Data Science

Paul A. Jensen

University of Illinois at Urbana-Champaign

• Introduction
• 0.1 Notation
• 1 Fields and Vectors
  • 1.1 Algebra
  • 1.2 The Field Axioms
  • 1.2.1 Common Fields in Mathematics
  • 1.3 Vector Addition
  • 1.4 Vector Multiplication is not Elementwise
  • 1.4.1 Do We Need Multiplication?
  • 1.5 Linear Systems
  • 1.6 Vector Norms
  • 1.6.1 Normalized (Unit) Vectors
  • 1.7 Scalar Vector Multiplication
  • 1.8 Inner (Dot) Products
  • 1.8.1 Computing the Dot Product
  • 1.8.2 Dot Product Summary
• 2 Matrices
  • 2.1 Matrix Multiplication
  • 2.1.1 Generalized Multiplication
  • 2.2 Identity Matrix
  • 2.3 Matrix Transpose
  • 2.4 Solving Linear Systems
  • 2.5 Gaussian Elimination
  • 2.6 Computational Complexity of Gaussian Elimination
  • 2.7 Solving Linear Systems in Matlab
• 3 The Finite Di↵erence Method
  • 3.1 Finite Di↵erences
  • 3.2 Linear Di↵erential Equations
  • 3.3 Discretizing a Linear Di↵erential Equation
  • 3.4 Boundary Conditions
• 4 Inverses, Solvability, and Rank
  • 4.1 Matrix Inverses
  • 4.2 Elementary Matrices
  • 4.3 Proof of Existence for the Matrix Inverse
  • 4.4 Computing the Matrix Inverse
  • 4.5 Numerical Issues
  • 4.6 Inverses of Elementary Matrices
  • 4.7 Rank
  • 4.8 Rank and Matrix Inverses
  • 4.9 Summary