Galois Theory and Advanced Linear Algebra

✍ Scribed by Rajnikant Sinha

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 357
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-ix
Galois Theory I (Rajnikant Sinha)....Pages 1-90
Galois Theory II (Rajnikant Sinha)....Pages 91-166
Linear Transformations (Rajnikant Sinha)....Pages 167-253
Sylvester’s Law of Inertia (Rajnikant Sinha)....Pages 255-349
Back Matter ....Pages 351-351