1Chapter-1
46Conclusion: References
2Introduction to Linear Algebra
47Chapter-6
31.1 Matrices and Vectors
48Linear Transformations
41.2 Systems of Linear Equations
496.1 Introduction to Linear Transformations
51.3 Matrix Operations
506.2 Matrix Representation of Linear Transformations
61.4 Linear Transformations
516.3 Kernel and Range of a Linear Transformation
71.5 Applications of Linear Algebra
526.4 Isomorphisms
81.6 Notation and Terminology: References
536.5 Compositions of Linear Transformations
9Chapter-2
546.6 Invertible Linear Transformations
10Vectors and Vector Spaces
55Conclusion: References
112.1 Introduction to Vectors
56Chapter-7
122.2 Vector Operations
57Eigenvalues and Eigenvectors
132.3 Vector Spaces
587.1 Introduction to Eigenvalues and Eigenvectors
142.4 Subspaces
597.2 Characteristic Polynomial
152.5 Span and Linear Independence
607.3 Diagonalization
162.6 Basis and Dimension
617.4 Similarity of Matrices
172.7 Coordinate Vectors: References
627.5 Applications of Eigenvalues and Eigenvectors
18Chapter-3
63Conclusion: References
19Matrix Algebra
64Chapter-8
203.1 Types of Matrices
65Inner Product Spaces
213.2 Matrix Operations
668.1 Definition and Examples of Inner Product Spaces
223.3 Matrix Multiplication
678.2 Norm and Distance
233.4 Inverse of a Matrix
688.3 Orthogonality
243.5 Elementary Row Operations
698.4 Orthogonal Complements
253.6 Determinants
708.5 Gram-Schmidt Process
263.7 Properties of Determinants
718.6 Orthogonal Matrices
27Conclusion
72Conclusion: References
28References
73Chapter-9
29Chapter-4
74Orthogonal Projections and Least Squares
30Systems of Linear Equations
759.1 Orthogonal Projections
314.1 Introduction to Systems of Linear Equations
769.2 Least Squares Approximations
324.2 Gaussian Elimination
779.3 Normal Equations
334.3 Gauss-Jordan Elimination
789.4 Orthogonal Matrices and Projections
344.4 Homogeneous and Non-Homogeneous Systems
799.5 Applications of Least Squares
354.5 Existence and Uniqueness of Solutions
80Conclusion: References
364.6 Applications of Systems of Linear Equations
81Chapter-10
37Conclusion: References
82Determinants and their Properties
38Chapter-5
8310.1 Definition and Evaluation of Determinants
39Vector Spaces and Subspaces
8410.2 Properties of Determinants
405.1 Definition and Examples of Vector Spaces
8510.3 Cramer’s Rule
415.2 Subspaces
8610.4 Inverse of a Matrix using Determinants
425.3 Linear Combinations and Span
8710.5 Applications of Determinants
435.4 Linear Independence
88Conclusion: References
445.5 Basis and Dimension
89Glossary
455.6 Change of Basis
90Index
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