Linear algebra
著者
書誌事項
Linear algebra
（Courant lecture notes in mathematics, 30）
Courant Institute of Mathematical Sciences, New York University , American Mathematical Society, c2020
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注記
Includes bibliographical reference (p. 289)
内容説明・目次
内容説明
This book is the second of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Both volumes have been used for several years in a one-year course sequence, Linear Algebra I and II, offered at New York University's Courant Institute.
The first three chapters of this second volume round out the coverage of traditional linear algebra topics: generalized eigenspaces, further applications of Jordan form, as well as bilinear, quadratic, and multilinear forms. The final two chapters are different, being more or less self-contained accounts of special topics that explore more advanced aspects of modern algebra: tensor fields, manifolds, and vector calculus in Chapter 4 and matrix Lie groups in Chapter 5. The reader can choose to pursue either chapter. Both deal with vast topics in contemporary mathematics. They include historical commentary on how modern views evolved, as well as examples from geometry and the physical sciences in which these topics are important. The book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved.
目次
Generalized Eigenspaces and the Jordon Decomposition
Further Applications of Jordon Form
Bilinear, Quadratic, and Multilinear Forms
Tensor Fields, Manifolds, and Vector Calculus
Matrix Lie Groups
Bibliography.
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