Линейная алгебра — раздел алгебры, изучающий объекты линейной природы:
векторные (или линейные) пространства,
линейные отображения,
системы линейных уравнений.
Среди основных инструментов, используемых в линейной алгебре — определители, матрицы, сопряжение.Теория инвариантов и тензорное исчисление обычно (в целом или частично) также считаются составными частями линейной алгебры.Такие объекты как квадратичные и билинейные формы, тензоры и операции как тензорное произведение непосредственно вытекают из изучения линейных пространств, но как таковые относятся к полилинейной алгебре.Основные конструкции линейной алгебры:
3rd edition. — Springer, 2012. — 167 p. — ISBN: 1447127382
Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution...
De Gruyter, 2023. — 292 p. — ISBN-13: 978-3-11-113591-5. There are numerous linear algebra textbooks available on the market. Yet, there are few that approach the notion of eigenvectors and eigenvalues across an operator’s minimum polynomial. In this book, we take that approach. This book provides a thorough introduction to the fundamental concepts of linear algebra. The...
2nd Edition. — Jones & Bartlett Learning, 2011. — 624 p. — ISBN-13: 978-1-4496-1352-5. Ward Cheney and David Kincaid have developed Linear Algebra: Theory and Applications, Second Edition, a multi-faceted introductory textbook, which was motivated by their desire for a single text that meets the various requirements for differing courses within linear algebra. For...
5th Edition. — Pearson Education, Inc., 2019. — 608 p. — ISBN: 9780134860244. This acclaimed theorem-proof text presents a careful treatment of the principal topics of linear algebra. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate. Applications to such...
Springer, 2021. — 492 p. — ISBN 978-3-030-52810-2. This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of...
2nd Edition. — Wiley, 2007. — 392 p. — (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts). — ISBN 0-471-75156-1, 978-0-471-75156-4. Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications...
Springer, 2024. — ISBN 10 3662679442; ISBN 13 9783662679449. Dieses Lehrbuch über die Lineare Algebra deckt den gesamten Stoff der zweisemestrigen Grundvorlesung ab. Seine anschauliche und konsequent matrizenorientierte Herangehensweise ermöglicht Studierenden ein intuitives Verständnis der abstrakten Objekte. Die im Buch präsentierten vielfältigen Anwendungen und Beispiele...
Cesar Lopez Perez, 2016. — 233 p. — ASIN: B01AFO8MAU Mathematica is a scientific computing software widely used in the experimental sciences. This book develops Mathematica applications in the field of linear algebra. The topics are illustrated with many examples and exercises solved. The following topics are covered: Variables And Functions Variables Functions Definition...
De Gruyter GmbH, 2017. — 450 p. — ISBN-13: 978-3-11-056259-0. Basic properties of vectors, matrices, determinants, eigenvalues and eigenvectors are discussed. Then, applications of matrices and determinants to various areas of statistical problems such as principal components analysis, model building, regression analysis, canonical correlation analysis, design of experiments...
De Gruyter, 2025. — 274 p. — ISBN 3111515702. This book is a comprehensive guide to Linear Algebra and covers all the fundamental topics such as vector spaces, linear independence, basis, linear transformations, matrices, determinants, inner products, eigenvectors, bilinear forms, and canonical forms. It also introduces concepts such as fields, rings, group homomorphism, and...
Springer, 2018. — 348 p. — ISBN 9789811309250. This book introduces the fundamental concepts, techniques and results of linear algebra that form the basis of analysis, applied mathematics and algebra. Intended as a text for undergraduate students of mathematics, science and engineering with a knowledge of set theory, it discusses the concepts that are constantly used by...
Wiley, 2021. — 464 p. — ISBN 978-1119437444. Linear Algebra delivers a fulsome exploration of the central concepts in linear algebra, including multidimensional spaces, linear transformations, matrices, matrix algebra, determinants, vector spaces, subspaces, linear independence, basis, inner products, and eigenvectors. While the text provides challenging problems that engage...
Springer, 2024. — 410 p. — ISBN 978-3-031-64908-0. This textbook provides a full treatment of Linear Algebra devoted to undergraduate and graduate physics students. Although the mathematical level is similar to the corresponding mathematical textbooks in regard to definitions, propositions and proofs, it adopts a language and approach more attuned to the reader’s familiarity...
2nd edition. — Minireference Co., 2020. — 518 p. — ISBN 9780992001025. Linear algebra is the foundation of science and engineering. Knowledge of linear algebra is a prerequisite for studying statistics, machine learning, computer graphics, signal processing, chemistry, economics, quantum mechanics, and countless other applications. Indeed, linear algebra offers a powerful...
2nd edition. — Dover, 2011. — 400 p. — ISBN: 0486482200
This unique text provides students with a basic course in both calculus and analytic geometry — no competitive editions cover both topics in a single volume. Its prerequisites are minimal, and the order of its presentation promotes an intuitive approach to calculus. Algebraic concepts receive an unusually strong emphasis....
Stylus Publishing, LLC, 2019. — 181 p. — ISBN: 978-1-683923-76-3. The aim of this book is two-fold: to introduce the fundamental concepts of linear algebra and to apply the theorems in computation-oriented applications. The book is suitable for a one semester course in linear algebra that can be used in a variety of contexts. The presentation of the material combines...
CRC Press, 2021. — 376 p. — (Textbooks in Mathematics). — ISBN 978-0367248963. Linear Algebra: An Inquiry-based Approach is written to give instructors a tool to teach students to develop a mathematical concept from first principles. The Inquiry-based Approach is central to this development. The text is organized around and offers the standard topics expected in a first...
Springer International Publishing, 2024. — 202 p. — (Compact Textbooks in Mathematics). — ISBN 978-3-031-54908-3. This textbook explores applications of linear algebra in data science at an introductory level, showing readers how the two are deeply connected. The authors accomplish this by offering exercises that escalate in complexity, many of which incorporate MatLAB....
Уважаемые: администратор, модераторы, доверенные пользователи и DosiaHeDeine. Я благодарен Вам за создание подраздела Матрицы и определители. Гораздо легче стало работать. Да благословит Вас Господь. С уважением, mian52
У нас в подразделе Линейная алгебра - 286 книг, и все они - разной тематики. Я предлагаю в подразделе Линейная алгебра (раздела Алгебра), создать новый подраздел: Матрицы и Определители. ...
Уважаемые: администратор, модераторы, доверенные пользователи и DosiaHeDeine. Я благодарен Вам за создание этого подраздела -Линейная алгебра. Результат этого - легче стало работать в разделе Алгебра, ведь это - 285 томов книг. Надеюсь, что таким образом, постепенно реорганизуем почти весь раздел Математика (совместными усилиями, разумеется). Да благословит Вас Господь, друзья, в этом деле благом. С уважением, mian52
Комментарии
Я благодарен Вам за создание подраздела Матрицы и определители. Гораздо легче стало работать.
Да благословит Вас Господь.
С уважением, mian52
Я предлагаю в подразделе Линейная алгебра (раздела Алгебра), создать новый подраздел: Матрицы и Определители.
...
Я благодарен Вам за создание этого подраздела -Линейная алгебра. Результат этого - легче стало работать в разделе Алгебра, ведь это - 285 томов книг. Надеюсь, что таким образом, постепенно реорганизуем почти весь раздел Математика (совместными усилиями, разумеется). Да благословит Вас Господь, друзья, в этом деле благом.
С уважением, mian52