Introduction to Linear Algebra, Defranza & Gigliardi
Chapter1 Systems of Linear Equations and Matrices 1-1.1 Systems of Linear Equations
Exercise Set 1.1
-1.2 Matrices and Elementary Row Operations
Exercise Set 1.2
-1.3 Matrix Algebra
Exercise Set 1.3
-1.4 The Inverse of a Square Matrix
Exercise Set 1.4
-1.5 Matrix Equations
Exercise Set 1.5
-1.6 Determinants
Exercise Set 1.6
-1.7 Elementary Matrices and LU Factorization
Exercise Set 1.7
-1.8 Applications of Systems of Linear Equatio
Exercise Set 1.8
Review Exercises
Chapter Test
Chapter2 Linear Combinations and Linear Independence-2.1 Vectors in Rn
Exercise Set 2.1
-2.2 Linear Combinations
Exercise Set 2.2
-2.3 Linear Independence
Exercise Set 2.3
Review Exercises
Chapter Test
Chapter3 Vector Spaces-3.1 Definition of a Vector Space
Exercise Set 3.1
-3.2 Subspaces
Exercise Set 3.2
-3.3 Basis and Dimension
Exercise Set 3.3
-3.4 Coordinates and Change of Basis
Exercise Set 3.4
-3.5 Application : Differential Equations
Exercise Set 3.5
Review Exercises
Chapter Test
Chapter4 Linear Transformations -4.1 Linear Transformations
Exercise Set 4.1
-4.2 The Null Space and Range
Exercise Set 4.2
-4.3 Isomorphisms
Exercise Set 4.3
-4.4 Matrix Representation of a Linear Transformation
Exercise Set 4.4
-4.5 Similarity
Exercise Set 4.5
-4.6 Application : Computer Graphics
Exercise Set 4.6
Review Exercises
Chapter Test
Chapter5 Eigenvalues and Eigenvectors-5.1 Eigenvalues and Eigenvectors
Exercise Set 5.1
-5.2 Diagonalization
Exercise Set 5.2
-5.3 Application : Systems of Linear Different
Exercise Set 5.3
-5.4 Application : Markov Chains
Exercise Set 5.4
Review Exercises
Chapter Test
Chapter6 Inner Product Spaces-6.1 The Dot Product on Rn
Exercise Set 6.1
-6.2 Inner Product Spaces
Exercise Set 6.2
-6.3 Orthonormal Bases
Exercise Set 6.3
-6.4 Orthogonal Complements
Exercise Set 6.4
-6.5 Application : Least Squares Approximation
Exercise Set 6.5
-6.6 Diagonalization of Symmetric Matrices
Exercise Set 6.6
-6.7 Application : Quadratic Forms
Exercise Set 6.7
-6.8 Application : Singular Value Decomposition
Exercise Set 6.8
Review Exercises
Chapter Test
A Preliminaries
A.1 Algebra of Sets
Exercise Set A.1
A.2 Functions
Exercise Set A.2
A.3 Techniques of Proof
Exercise Set A.3
A.4 Mathematical Induction
Exercise Set A.4
Answers to Odd-Numbered Exercises
A.3 Techniques of Proof
Exercise Set A.3
A.4 Mathematical Induction
Exercise Set A.4
Answers to Odd-Numbered Exercises
