Lecture Notes
Linear Algebra
Much part of these lecture notes came from Linear Algebra course I taught.
These lecture notes should be accessible by undergraduate students of mathematics or physics who have taken Set Theory and Calculus series.
Lecture Notes
Problem Sets
References and Further Reading
Click on linked topics to view lecture notes.
Vector Spaces
Linear Combination
Linear Independence
Rank of a Matrix
Linear Maps
The Kernel and Image of a Linear Map
The Matrix Associated with a Linear Map
Composition of Linear Maps
Inverses
Scalar Products
Orthogonal Bases
Determinants I: Determinants of Order 2
Determinants II: Determinants of Order \(n\)
Rank of a Matrix 2: The Rank of a Matrix and Subdeterminants
Cramer's Rule
Inverse of a Matrix
Determinants as Area and Volume
Square Roots of Operators
Square Roots of Operators II
Click on the following links for problems.
Sheldon Axler, Linear Algebra Done Right, Third Edition, Springer, 2015
Serge Lang, Introduction to Linear Algebra, Second Edition, Springer, 1986
Serge Lang, Linear Algebra, Third Edition, Springer, 2004