Galois theory and advanced linear algebra
著者
書誌事項
Galois theory and advanced linear algebra
Springer, 〓2020
機械可読データファイル（リモートファイル）
注記
Includes bibliographical references
収録内容
- Intro
- Preface
- Contents
- About the Author
- 1 Galois Theory I
- 1.1 Euclidean Rings
- 1.2 Polynomial Rings
- 1.3 The Eisenstein Criterion
- 1.4 Roots of Polynomials
- 1.5 Splitting Fields
- Exercises
- 2 Galois Theory II
- 2.1 Simple Extensions
- 2.2 Galois Groups
- 2.3 Applications of Galois Theory
- 2.4 Solvability By Radicals
- 3 Linear Transformations
- 3.1 Eigenvalues
- 3.2 Canonical Forms
- 3.3 The Cayley-Hamilton Theorem
- 4 Sylvester's Law of Inertia
- 4.1 Positive Definite Matrices
- 4.2 Sylvester's Law
- 4.3 Application to Riemannian Geometry
内容説明・目次
内容説明
This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley-Hamilton theorem, Galois groups, Sylvester's law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial.
目次
Galois Theory I.- Galois Theory II.- Linear Transformations.- Sylvester's Law of Inertia.- Bibliography.
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