Linear Algebra: Core Topics For The Second Course

This is a book for a 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. This is highly effective to create the needed depth of understanding a general theory by detailing a proof of a particular case that encapsulates the main idea of a general theorem. Using the knowledge gained from a particular case, it 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.