Linear algebra
著者
書誌事項
Linear algebra
（The Sally series, . Pure and applied undergraduate texts ; 45）
American Mathematical Society, c2020
- : [pbk.]
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注記
Includes bibliographical references (p. 301-302) and index
内容説明・目次
内容説明
This text develops linear algebra with the view that it is an important gateway connecting elementary mathematics to more advanced subjects, such as advanced calculus, systems of differential equations, differential geometry, and group representations. The purpose of this book is to provide a treatment of this subject in sufficient depth to prepare the reader to tackle such further material. The text starts with vector spaces, over the sets of real and complex numbers, and linear transformations between such vector spaces. Later on, this setting is extended to general fields. The reader will be in a position to appreciate the early material on this more general level with minimal effort. Notable features of the text include a treatment of determinants, which is cleaner than one often sees, and a high degree of contact with geometry and analysis, particularly in the chapter on linear algebra on inner product spaces. In addition to studying linear algebra over general fields, the text has a chapter on linear algebra over rings. There is also a chapter on special structures, such as quaternions, Clifford algebras, and octonions.
目次
Vector spaces, linear transformations, and matrices
Eigenvalues, eigenvectors, and generalized eigenvectors
Linear algebra on inner product spaces
Further basic concepts: duality, convexity, positivity
Multilinear algebra
Linear algebra over more general fields
Rings and modules
Special structures in linear algebra
Complementary results
Bibliography
Index.
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