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Gantmacher's Masterpiece on Matrix Theory: Download and Read for Free in DJVU Format



Gantmacher Theory of Matrices: A Free and Comprehensive Resource




Introduction




If you are interested in learning more about matrix theory, one of the most fundamental and versatile branches of mathematics, you may want to check out a classic book by F.R. Gantmacher, Theory of Matrices. This book, originally published in Russian in 1953 and translated into English in 1959, is widely regarded as one of the most comprehensive and authoritative texts on the subject. In this article, we will introduce you to Gantmacher's book, show you how to access it for free online in DJVU format, and give you some tips on how to use it effectively for your learning.




gantmacher theory of matrices djvu free



What is matrix theory and why is it important?




A matrix is a rectangular array of numbers or symbols that can be used to represent various mathematical objects and operations. Matrix theory is the study of matrices and their properties, such as determinants, inverses, eigenvalues, eigenvectors, rank, trace, etc. Matrix theory also explores how matrices can be used to solve various problems in linear algebra, such as systems of linear equations, linear transformations, vector spaces, bases, orthogonality, etc.


Matrix theory is important because it has many applications in various fields of science and engineering, such as physics, chemistry, biology, computer science, electrical engineering, mechanical engineering, etc. For example, matrices can be used to model physical phenomena such as rotations, vibrations, waves, quantum mechanics, relativity, etc. Matrices can also be used to perform computations such as matrix multiplication, inversion, decomposition, etc., which are essential for numerical analysis, optimization, machine learning, data mining, image processing, etc.


Who was Gantmacher and what did he contribute to matrix theory?




Felix Ruvimovich Gantmacher (1908-1990) was a Soviet mathematician who specialized in matrix theory and its applications. He was a professor at Moscow State University and Moscow Institute of Physics and Technology. He was also a corresponding member of the Soviet Academy of Sciences and a recipient of several awards and honors.


Gantmacher made significant contributions to various aspects of matrix theory, such as matrix calculus, canonical forms, stability theory, perturbation theory, matrix inequalities, functions of matrices, etc. He also wrote several books and papers on these topics, including his two-volume masterpiece Theory of Matrices, which is considered one of the most comprehensive and authoritative texts on the subject.


What are the main topics covered in his book Theory of Matrices?




Theory of Matrices by Gantmacher consists of two volumes, each containing seven or eight chapters. The first volume covers the following topics:



  • Basic concepts and definitions of matrices and linear operators



  • Theoretical and practical methods of solving systems of linear equations



  • Characteristic and minimal polynomials of matrices and their applications



  • Functions of matrices and their properties



  • Canonical forms of matrices and linear operators



  • Matrix norms and inequalities



  • Stability theory of linear systems



  • Perturbation theory of matrices and eigenvalues



The second volume covers the following topics:



  • Matrix calculus and its applications



  • Linear spaces and linear transformations



  • Bilinear and quadratic forms



  • Orthogonal and unitary transformations



  • Hermitian and skew-Hermitian matrices



  • Positive definite and semi-definite matrices



  • Non-negative matrices and Perron-Frobenius theory



  • Commuting and anti-commuting matrices



The book also contains numerous examples, exercises, and references for further reading.


How to access Gantmacher's book for free




What is DJVU format and how to read it?




DJVU is a file format that is designed to store scanned documents, especially those containing a combination of text, line drawings, and photographs. DJVU files are typically smaller than PDF files, but retain a high quality of image compression. DJVU files can be viewed using various software applications, such as WinDjView, DjVuLibre, or Sumatra PDF. You can also use online tools such as DjVu Viewer or DjVu to PDF Converter to open or convert DJVU files.


Where to find the online versions of Gantmacher's book?




You can find the online versions of Gantmacher's book in DJVU format on several websites, such as Archive.org, School of Mathematics at the University of Edinburgh, or Mathnet.ru. Here are the links to the first and second volumes of the book:



Volume 1Volume 2


https://archive.org/details/theoryofmatrices00ganthttps://archive.org/details/theoryofmatrices02gant


https://www.maths.ed.ac.uk/v1ranick/papers/gantmacher1.pdfhttps://www.maths.ed.ac.uk/v1ranick/papers/gantmacher2.pdf


http://www.mathnet.ru/php/getFT.phtml?jrnid=rm&paperid=5878&what=fullt&option_lang=enghttp://www.mathnet.ru/php/getFT.phtml?jrnid=rm&paperid=5879&what=fullt&option_lang=eng


How to download and save the book for offline use?




If you want to download and save the book for offline use, you can follow these steps:



  • Choose one of the links above and open it in your browser.



  • Right-click on the page and select "Save as" or "Download as".



  • Choose a location on your computer where you want to save the file.



  • Select "DJVU" as the file type and click "Save".



  • Repeat the same steps for the other volume of the book.



  • You can now open the files using any DJVU viewer or converter.



How to use Gantmacher's book effectively




What are the prerequisites and level of difficulty of the book?




What are the prerequisites and level of difficulty of the book?




Gantmacher's book is meant for advanced undergraduate or graduate students in mathematics or related fields who have some background in linear algebra and abstract algebra. The book assumes that the reader is familiar with basic concepts and results of matrices and linear operators, such as determinants, inverses, eigenvalues, eigenvectors, rank, trace, etc. The book also uses some notions and techniques from set theory, logic, analysis, and algebra, such as sets, functions, relations, equivalence classes, groups, rings, fields, polynomials, limits, continuity, differentiation, integration, etc. The book does not require any knowledge of calculus, but some familiarity with differential equations and complex analysis may be helpful for some topics.


The book is not an easy read, as it covers a lot of material in depth and rigor. The book also contains many exercises that range from simple computations to challenging proofs. The book requires a high level of mathematical maturity and abstraction from the reader. However, the book also provides many examples, explanations, and motivations for the concepts and results. The book is a valuable resource for anyone who wants to learn matrix theory thoroughly and systematically.


How to navigate through the book and find relevant information?




The book is organized into two volumes, each containing seven or eight chapters. Each chapter is divided into several sections, each containing a main theorem or result, followed by its proof or derivation, and then by some corollaries or applications. Each section also contains some remarks or comments that provide additional insights or historical notes on the topic. At the end of each section, there are several exercises that test the reader's understanding and skills on the topic.


To navigate through the book and find relevant information, the reader can use the table of contents, the index, and the references provided at the beginning and end of each volume. The table of contents gives an overview of the main topics covered in each chapter and section. The index lists the keywords and terms used in the book, along with their page numbers. The references provide a list of books and papers that are cited or consulted by the author, along with their bibliographic information.


The reader can also use the cross-references within the text to locate related topics or results. The author uses various symbols and abbreviations to indicate cross-references, such as (I.2.3) for Theorem 3 in Section 2 of Chapter I, or [5] for Reference 5 at the end of Volume I. The reader can also use footnotes to find additional information or explanations on certain points.


How to supplement the book with other sources and exercises?




Although Gantmacher's book is very comprehensive and authoritative on matrix theory, the reader may want to supplement it with other sources and exercises to enhance their learning experience. Some possible ways to do this are:



  • Compare Gantmacher's book with other books on matrix theory, such as Linear Algebra Done Right by Sheldon Axler, Matrix Analysis by Roger Horn and Charles Johnson, or Matrix Computations by Gene Golub and Charles Van Loan. These books may have different approaches, notations, or perspectives on matrix theory, and may cover some topics that are not included in Gantmacher's book.



  • Consult online resources on matrix theory, such as MIT OpenCourseWare Linear Algebra course by Gilbert Strang, Khan Academy Linear Algebra videos by Sal Khan, or Math Stack Exchange Linear Algebra questions and answers by various users. These resources may provide more examples, explanations, or applications of matrix theory, and may also offer interactive features such as quizzes or forums.



  • Solve more exercises on matrix theory, such as those from Schaum's Outline of Linear Algebra by Seymour Lipschutz and Marc Lipson, Linear Algebra Problem Book by Paul Halmos, or Problems and Solutions in Matrix Theory by Charles Johnson. These exercises may provide more practice and challenge on matrix theory, and may also cover some topics that are not included in Gantmacher's book.



Conclusion




Summary of the main points




In this article, we have introduced you to Gantmacher's book Theory of Matrices, a classic and comprehensive text on matrix theory and its applications. We have shown you how to access it for free online in DJVU format, and how to use it effectively for your learning. We have also given you some tips on how to supplement it with other sources and exercises.


Benefits and challenges of using Gantmacher's book




Using Gantmacher's book has many benefits and challenges for the reader who wants to learn matrix theory. Some of the benefits are:



  • The book covers a lot of material in depth and rigor, providing a solid foundation and understanding of matrix theory.



  • The book explores many applications of matrix theory in various fields of science and engineering, showing the relevance and usefulness of matrix theory.



  • The book contains many exercises that range from simple computations to challenging proofs, offering a lot of practice and challenge for the reader.



Some of the challenges are:



  • The book assumes a high level of mathematical maturity and abstraction from the reader, requiring a lot of concentration and effort to follow the arguments and proofs.



  • The book uses some notions and techniques from other branches of mathematics that may not be familiar to the reader, requiring some additional background or review.



  • The book is not an easy read, as it covers a lot of material in a dense and concise way, requiring a lot of patience and perseverance from the reader.



Recommendations and tips for further learning




If you are interested in learning more about matrix theory or related topics, here are some recommendations and tips for further learning:



  • Review the concepts and results of matrix theory regularly, as they are interconnected and build upon each other.



  • Try to solve as many exercises as possible from Gantmacher's book or other sources, as they will help you consolidate your knowledge and skills on matrix theory.



  • Seek help or feedback from others who are also learning or teaching matrix theory, such as your classmates, instructors, tutors, or online communities.



  • Explore other topics or applications of matrix theory that interest you, such as numerical linear algebra, linear programming, graph theory, cryptography, etc.



  • Keep an open mind and enjoy the beauty and elegance of matrix theory!



FAQs




Here are some frequently asked questions about Gantmacher's book Theory of Matrices:



  • Q: How can I get a hard copy of Gantmacher's book?



  • A: You can try to find a used copy of Gantmacher's book on online platforms such as Amazon, eBay, or AbeBooks. You can also try to borrow a copy from your local library or university library. Alternatively, you can print out the DJVU files of the book if you have access to a printer.



  • Q: How can I cite Gantmacher's book in my academic work?



  • A: You can use the following citation format for Gantmacher's book:



Gantmacher, F.R. (1959). Theory of Matrices. Vols. 1-2. New York: Chelsea Publishing Company.



  • Q: How can I contact the author of Gantmacher's book?



  • A: Unfortunately, you cannot contact the author of Gantmacher's book, as he passed away in 1990. However, you can try to contact his former colleagues or students who may have known him personally or professionally.



  • Q: How can I give feedback or suggestions on Gantmacher's book?



  • A: You can give feedback or suggestions on Gantmacher's book by writing a review or comment on the websites where you accessed the book, such as Archive.org, School of Mathematics at the University of Edinburgh, or Mathnet.ru. You can also share your feedback or suggestions with other readers or learners who are using Gantmacher's book.



  • Q: How can I donate or support Gantmacher's book?



  • A: You can donate or support Gantmacher's book by making a contribution to the organizations that host or provide access to the book online, such as Archive.org, School of Mathematics at the University of Edinburgh, or Mathnet.ru. You can also donate or support Gantmacher's book by spreading the word about it to others who may be interested in learning matrix theory.



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