# Learn Linear Algebra with Gerd Fischer's Book (PDF Download)

## Gerd Fischer Lineare Algebra Pdf 13

If you are looking for a comprehensive and accessible introduction to linear algebra, you might want to check out Gerd Fischer Lineare Algebra, a popular textbook written by Gerd Fischer, a professor of mathematics at the Technical University of Munich. In this article, we will give you an overview of what this book is about, what topics it covers, how it is structured and written, who it is for and how it can be used, and how you can access it online.

## Gerd Fischer Lineare Algebra Pdf 13

## What is linear algebra?

Linear algebra is a branch of mathematics that studies linear equations, matrices, vectors, vector spaces, linear transformations, determinants, eigenvalues, inner products, orthogonality, linear groups, representations, and other related concepts. Linear algebra is essential for understanding many areas of mathematics, such as algebra, geometry, analysis, differential equations, numerical analysis, optimization, graph theory, cryptography, etc. Linear algebra also has many applications in physics, engineering, computer science, economics, biology, chemistry, social sciences, and more.

## What are the main topics covered in the book?

### Vector spaces and linear maps

The first part of the book introduces the basic concepts of vector spaces and linear maps. A vector space is a set of objects (called vectors) that can be added together and multiplied by scalars (numbers). A linear map is a function that preserves addition and scalar multiplication between two vector spaces. The book explains how to define and work with vector spaces and linear maps using examples from geometry, algebra, analysis, physics, etc. The book also introduces matrices as a way of representing linear maps between finite-dimensional vector spaces. The book then discusses how to compute determinants (a measure of how a linear map changes area or volume) and eigenvalues (a measure of how a linear map stretches or shrinks vectors) using matrices.

### Inner product spaces and orthogonality

The second part of the book covers inner product spaces and orthogonality. An inner product space is a vector space that has an additional operation (called an inner product) that allows us to measure angles and lengths of vectors. Orthogonality is a property that means two vectors are perpendicular to each other (have a right angle between them). The book shows how to define and work with inner product spaces using examples from geometry, analysis, physics, etc. The book also introduces the Gram-Schmidt process (a method of finding an orthogonal basis for a vector space), orthogonal matrices (matrices that preserve angles and lengths), and quadratic forms (functions that involve squares of variables).

### Linear groups and representations

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## Conclusion

In conclusion, Gerd Fischer Lineare Algebra is a great book for anyone who wants to learn linear algebra in a comprehensive and accessible way. The book covers all the essential topics of linear algebra as well as some more advanced topics that are usually not found in other introductory books. The book is written in a clear and concise style, with an emphasis on explaining the concepts and ideas rather than on technical details or formalism. The book uses a lot of examples and diagrams to illustrate the topics and to show their applications and connections to other areas of mathematics and science. The book also uses a lot of analogies and metaphors to make the topics more accessible and intuitive for the reader. The book tries to balance between rigor and simplicity, between abstraction and concreteness, between generality and specificity.

The book is intended for students who are taking a two-semester course on linear algebra at the undergraduate level. The book assumes that the reader has some basic knowledge of calculus, set theory, logic, and elementary algebra. The book aims to provide a solid foundation for further studies in mathematics and other sciences that require linear algebra. The book also aims to develop the reader's skills in abstract thinking, logical reasoning, problem-solving, and mathematical communication.

The book can be used as a textbook for a linear algebra course or as a reference for self-study or revision. The book offers a lot of flexibility for the instructor or the reader to choose which topics to focus on or to skip according to their interests and needs. The book also offers a lot of guidance and feedback for the reader through its exercises and solutions.

If you want to access the book online, you have several options. You can download or view the PDF version of the book from various sources, such as the official website of the publisher, the Internet Archive, the E-Bookshelf, or __eBooks.com__. However, please note that some of these sources may require you to pay a fee or register an account before you can access the book. Also, please respect the copyright of the author and the publisher and do not distribute or reproduce the book without their permission.

We hope that this article has given you a good overview of what Gerd Fischer Lineare Algebra is about and why you should read it if you are interested in learning linear algebra. We highly recommend this book for anyone who wants to master this important and fascinating branch of mathematics.

## FAQs

What is the difference between the 13th edition and the 17th edition of the book?

The 13th edition of the book was published in 2002 and the 17th edition was published in 2010. The main difference between them is that the 17th edition has been updated and revised to reflect the latest developments and changes in linear algebra. The 17th edition also has some new exercises and solutions, some new examples and diagrams, some new references and appendices, and some corrections and improvements in the text.

How long does it take to read the book?

The book has about 600 pages, so it depends on how fast you read and how much time you spend on each page. If you read about 20 pages per day, it would take you about a month to finish the book. However, if you want to fully understand and practice each topic, you may need to spend more time on each page and do more exercises and problems.

Is there an English translation of the book?

No, there is no English translation of the book available at the moment. The book is written in German and has not been translated into any other language yet. However, if you have some basic knowledge of German or use an online translator tool, you should be able to follow most of the text without much difficulty.

Is there an online course or video lecture based on the book?

No, there is no online course or video lecture based on the book available at the moment. The book is meant to be used as a textbook for a linear algebra course or as a reference for self-study or revision. However, if you are looking for some online resources to supplement your learning from the book, you may find some useful videos on YouTube or Khan Academy that cover similar topics.

Where can I buy a hard copy of the book?

If you want to buy a hard copy of the book, you have several options. You can order it from online retailers such as Amazon or eBay, or from local bookstores that sell academic books. You can also borrow it from libraries that have it in their collection. However, please note that some of these options may require you to pay a fee or wait for delivery or availability.