## Lecture Notes

### Linear Algebra

The intended purpose of these lecture notes is not in any way to attempt to provide in-depth discussions or any new insight on Linear Algebra but to provide beginners a quick crash course on basic ideas, compuational techniques, and applications of Linear Algebra so readers can advance more easily by filling in gaps with more in-depth knowledge from currently existing so many wonderful books on Linear Algebra.

These lecture notes should be accessible by undergraduate students of mathematics or physics who have taken Set Theory and Calculus series.

#### Lecture Notes

#### Homework

#### 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: Than Rank of a Matrix and Subdeterminants

Cramer's Rule

Inverse of a Matrix

Dterminants as Area and Volume

Click on the following links topics for homework.

Not in particular order. There are so many wonderful books on Functions of a Complex Variable. I have listed below only some of those books on Functions of a Complex Variable that I am familiar with.

Introduction to Linear Algebra, Second Edition, Serge Lang, Springer, 1986

Linear Algebra, Third Edition, Serge Lang, Springer, 2004