Lecture Notes for Math 4063-5023

Lecture Notes for Math 4063/5023 Advanced Linear Algebra

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Lecture 1: Introduction: Fields and Vector Spaces
Lecture 2: Subspaces, Linear Dependence and Linear Independence
Lecture 3: Dimension and Bases
Lecture 4: Elementary Operations and Matrices
Lecture 5: Finitely Generated Vector Spaces
Lecture 6: Systems of Linear Equations
Lecture 7; Solving Linear Systems
Lecture 8: Homogeneous Linear Systems
Lecture 9: Hyperplanes
Summary of the Basic Definitions and Theorems for Exam 1
Lecture 10: Linear Transformations
Lecture 11: Linear Transformations and Matrices
Lecture 12: Homomorphisms and Isomorphisms
Lecture 13: Quotient Spaces
Lecture 14: The Isomorphism Theorems
Lecture 15: Endomorphisms and Automorphisms
Lecture 16: Determinants
Lecture 17: The Theory of A Single Endomorphism (Introduction)
Lecture 18: Invariant Subspaces
Lecture 19: The Triangular Form and Cayley-Hamilton Theorems
Lecture 20:
Lecture 21: