## 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

Click on the following links for problems.

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

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