Advanced Linear Algebra With an Introduction to Module Theory

✍ Scribed by Shou-Te Chang

• Publisher: World Scientific Publishing
• Year: 2024
• Tongue: English
• Leaves: 274
• Category: Library

✦ Table of Contents

Contents
Preface
About the Author
Special Notes
1 Modules and Vector Spaces
1.1 Definitions and examples of modules and vector spaces
1.2 Linear combinations and linear independence
1.3 Bases
1.4 Dimension for finite dimensional vector spaces
1.5 Dimension for infinite dimensional vector spaces
1.6 More on cardinal arithmetic
2 Linear Maps
2.1 Linear maps
2.2 Quotient modules and quotient spaces
2.3 Matrices
3 Determinant
3.1 Basics of the determinant
3.2 Matrix operations
3.3 Reduced row echelon form and applications
3.4 Determinant and invertible matrices
3.5 Rank
4 Canonical Forms
4.1 Equivalent matrices
4.2 The normal form
4.3 Structure theorem of finitely generated modules over a PID
4.4 Invariance theorem
4.5 Rational canonical form
4.6 Jordan canonical form
5 A Brief Introduction to the Tensor Product
5.1 Bilinear maps and multilinear maps
5.2 Tensor products of vector spaces
5.3 Tensor products of modules
Index