LINEAR ALGEBRA: CORE TOPICS FOR THE SECOND COURSE

This is a book for the second course in linear algebra whereby students are assumed to be familiar with calculations using real matrices. To facilitate a smooth transition into rigorous proofs, it combines abstract theory with matrix calculations.

This book presents numerous examples and proofs of particular cases of important results before the general versions are formulated and proved. The knowledge gained from a particular case, that encapsulates the main idea of a general theorem, can be easily extended to prove another particular case or a general case. For some theorems, there are two or even three proofs provided. In this way, students stand to gain and study important results from different angles and, at the same time, see connections between different results presented in the book.

Contents:

• Preface
• Vector Spaces
• Linear Transformations
• Inner Product Spaces
• Reduction of Endomorphisms
• Appendices:
  • Permutations
  • Complex Numbers
  • Polynomials
  • Infinite Dimensional Inner Product Spaces

Readership: Undergraduate students taking a second course in linear algebra.

Key Features:

• Reading simpler and more manageable proofs is more likely to encourage students to work with proofs
• We believe that students should have at their disposal as many tools as possible when solving problems. For example, overcoming determinants when it comes to diagonalization and Jordan canonical form
• The explanations are clear and precise manner