LINEAR ALGEBRA: CORE TOPICS FOR THE SECOND COURSE

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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. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Vector Spaces 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.

LINEAR ALGEBRA: CORE TOPICS FOR THE FIRST COURSE

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The book is an introduction to linear algebra intended as a textbook for the first course in linear algebra. In the first six chapters we present the core topics: matrices, the vector space ℝn, orthogonality in ℝn, determinants, eigenvalues and eigenvectors, and linear transformations. The book gives students an opportunity to better understand linear algebra in the next three chapters: Jordan forms by examples, singular value decomposition, and quadratic forms and positive definite matrices. In the first nine chapters everything is formulated in terms of ℝn. This makes the ideas of linear algebra easier to understand. The general vector spaces are introduced in Chapter 10. The last chapter presents problems solved with a computer algebra system. At the end of the book we have results or solutions for odd numbered exercises. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Matrices Contents: Matrices The Vector Space ℝn Orthogonality in ℝn Determinants Eigenvalues and Eigenvectors Linear Transformations Jordan Forms by Examples Singular Value Decomposition Quadratic Forms and Positive Definite Matrices Vector Spaces Solutions with CAS Answers to Selected Exercises Readership: Undergraduate students taking a first course in linear algebra.