Essential Linear Algebra with Applications

A Problem-Solving Approach

  • Titu Andreescu

Table of contents

  1. Front Matter
    Pages i-x
  2. Titu Andreescu
    Pages 1-52
  3. Titu Andreescu
    Pages 53-83
  4. Titu Andreescu
    Pages 85-105
  5. Titu Andreescu
    Pages 107-148
  6. Titu Andreescu
    Pages 149-196
  7. Titu Andreescu
    Pages 197-235
  8. Titu Andreescu
    Pages 237-300
  9. Titu Andreescu
    Pages 339-375
  10. Titu Andreescu
    Pages 377-482
  11. Titu Andreescu
    Pages 483-490
  12. Back Matter
    Pages 491-491

About this book


This textbook provides a rigorous introduction to linear algebra in addition to material suitable for a more advanced course while emphasizing the subject’s interactions with other topics in mathematics such as calculus and geometry. A problem-based approach is used to develop the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality.

Key features include:

• a thorough presentation of the main results in linear algebra along with numerous examples to illustrate the theory;

 • over 500 problems (half with complete solutions) carefully selected for their elegance and theoretical significance;

• an interleaved discussion of geometry and linear algebra, giving readers a solid understanding of both topics and the relationship between them.


Numerous exercises and well-chosen examples make this text suitable for advanced courses at the junior or senior levels. It can also serve as a source of supplementary problems for a sophomore-level course. 



Cayley-Hamilton theorem Determinant Diagonalizable Duality Linear maps Linear systems Matrices Minimal polynomial Quadratic form Vector space

Authors and affiliations

  • Titu Andreescu
    • 1
  1. 1.Natural Sciences and MathematicsUniversity of Texas at DallasRichardsonUSA

Bibliographic information