Linear Algebra: Concepts and Techniques on Euclidean Spaces

Description

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