Linear Algebra: Concepts and Techniques on Euclidean Spaces

✍ Scribed by Ma Siu Lun, Ng Kah Loon, Victor Tan

• Publisher: McGraw-Hill Education
• Year: 2016
• Tongue: English
• Leaves: 246
• Edition: 2
• Category: Library

✦ Table of Contents

Chapter 1 Linear Systems and Gaussian Elimination
Section 1.1 Linear Systems and Their Solutions
Section 1.2 Elementary Row Operations
Section 1.3 Row-Echelon Forms
Section 1.4 Gaussian Elimination
Section 1.5 Homogeneous Linear Systems
Exercise 1
Chapter 2 Matrices
Section 2.1 Introduction to Matrices
Section 2.2 Matrix Operations
Section 2.3 Inverses of Square Matrices
Section 2.4 Elementary Matrices
Section 2.5 Determinants
Exercise 2
Chapter 3 Vector Spaces
Section 3.1 Euclidean n-Spaces
Section 3.2 Linear Combinations and Linear Spans
Section 3.3 Subspaces
Section 3.4 Linear Independence
Section 3.5 Bases
Section 3.6 Dimensions
Section 3.7 Transition Matrices
Exercise 3
Chapter 4 Vector Spaces Associated with Matrices
Section 4.1 Row Spaces and Column Spaces
Section 4.2 Ranks
Section 4.3 Nullspaces and Nullities
Exercise 4
Chapter 5 Orthogonality
Section 5.1 The Dot Product
Section 5.2 Orthogonal and Orthonormal Bases
Section 5.3 Best Approximations
Section 5.4 Orthogonal Matrices
Exercise 5
Chapter 6 Diagonalization
Section 6.1 Eigenvalues and Eigenvectors
Section 6.2 Diagonalization
Section 6.3 Orthogonal Diagonalization
Section 6.4 Quadratic Forms and Conic Sections
Exercise 6
Chapter 7 Linear Transformations
Section 7.1 Linear Transformations from R^n to R^m
Section 7.2 Ranges and Kernels
Section 7.3 Geometric Linear Transformations
Exercise 7
Index