Algebra 2: Linear Algebra, Galois Theory, Representation theory, Group extensions and Schur Multiplier

✍ Scribed by Ramji Lal (auth.)

• Publisher: Springer Singapore
• Year: 2017
• Tongue: English
• Leaves: 440
• Series: Infosys Science Foundation Series
• Edition: 1
• Category: Library

✦ Synopsis

This is the second in a series of three volumes dealing with important topics in algebra. Volume 2 is an introduction to linear algebra (including linear algebra over rings), Galois theory, representation theory, and the theory of group extensions. The section on linear algebra (chapters 1–5) does not require any background material from Algebra 1, except an understanding of set theory. Linear algebra is the most applicable branch of mathematics, and it is essential for students of science and engineering As such, the text can be used for one-semester courses for these students. The remaining part of the volume discusses Jordan and rational forms, general linear algebra (linear algebra over rings), Galois theory, representation theory (linear algebra over group algebras), and the theory of extension of groups follow linear algebra, and is suitable as a text for the second and third year students specializing in mathematics.

✦ Table of Contents

Front Matter....Pages i-xviii
Vector Spaces....Pages 1-30
Matrices and Linear Equations....Pages 31-71
Linear Transformations....Pages 73-95
Inner Product Spaces....Pages 97-129
Determinants and Forms....Pages 131-193
Canonical Forms, Jordan and Rational Forms....Pages 195-228
General Linear Algebra....Pages 229-263
Field Theory, Galois Theory....Pages 265-329
Representation Theory of Finite Groups....Pages 331-366
Group Extensions and Schur Multiplier....Pages 367-425
Back Matter....Pages 427-432

✦ Subjects

Linear and Multilinear Algebras, Matrix Theory;Associative Rings and Algebras;Commutative Rings and Algebras;Non-associative Rings and Algebras;Group Theory and Generalizations;Number Theory