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**About this book :- **
**Essential Linear Algebra with Applications A Problem Solving Approach ** written by
** Titu Andreescu **.
This textbook is intended for an introductory followed by an advanced course in linear algebra, with emphasis on its interactions with other topics in mathematics, such as calculus, geometry, and combinatorics. We took a straightforward path to the most important topic, linear maps between vector spaces, most of the time finite dimensional. However, since these concepts are fairly abstract and not necessarily natural at first sight, we included a few chapters with explicit examples of vector spaces such as the standard ndimensional vector space over a field and spaces of matrices. We believe that it is fundamental for the student to be very familiar with these spaces before dealing with more abstract theory. In order to maximize the clarity of the concepts discussed, we included a rather lengthy chapter on 2 2 matrices and their applications, including the theory of Pell’s equations.
This will help the student manipulate matrices and vectors in a concrete way before delving into the abstract and very powerful approach to linear algebra through the study of vector spaces and linear maps.

**Book Detail :- **
** Title: ** Essential Linear Algebra with Applications A Problem Solving Approach
** Edition: **
** Author(s): ** Titu Andreescu
** Publisher: ** Birkhäuser Basel
** Series: **
** Year: ** 2014
** Pages: ** 498
** Type: ** PDF
** Language: ** English
** ISBN: ** 978-0-8176-4360-7,978-0-8176-4636-3
** Country: ** US
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**About Author :- **
The author ** Titu Andreescu **
is an associate professor of mathematics at the University of Texas at Dallas.
He is firmly involved in mathematics contests and olympiads, having been the Director of American Mathematics Competitions (as appointed by the Mathematical Association of America[1]), Director of the Mathematical Olympiad Program, Head Coach of the United States International Mathematical Olympiad Team, and Chairman of the United States of America Mathematical Olympiad. He has also authored a large number of books on the topic of problem solving and olympiad style mathematics.

**All Famous Books of this Author :- **

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** • Download PDF Linear Algebra (Forth Edition) by Jim Hefferon **

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**Book Contents :- **
**Essential Linear Algebra with Applications A Problem Solving Approach ** written by
** Titu Andreescu **
cover the following topics.

1. Matrix Algebra

2. Square Matrices of Order 2

3. Matrices and Linear Equations

4. Vector Spaces and Subspaces

5. Linear Transformations

6. Duality

7. Determinants

8. Polynomial Expressions of Linear Transformations and Matrices

9. Diagonalizability

10. Forms

11. Appendix: Algebraic Prerequisites

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