ENGLISH

A First Course in Linear Algebra

By H. J. Woerdeman

Book information

Year
2021
ISBN
9780367697389, 9780367684730
Language
english
Format
PDF
Filesize
19 MB (19634374 bytes)
Pages
\284
Time added
2021-02-11 21:06:54

Description

Cover Half Title Series Page Title Page Copyright Page Dedication Contents Preface Preface to the Instructor Preface to the Student Acknowledgments Notation List of figures 1. Matrices and Vectors 1.1. Matrices and Linear Systems 1.2. Row Reduction: Three Elementary Row Operations 1.3. Vectors in Rn, Linear Combinations and Span 1.4. Matrix Vector Product and the Equation Ax = b 1.5. How to Check Your Work 1.6. Exercises 2. Subspaces in Rn, Basis and Dimension 2.1. Subspaces in Rn 2.2. Column Space, Row Space and Null Space of a Matrix 2.3. Linear Independence 2.4. Basis 2.5. Coordinate Systems 2.6. Exercises 3. Matrix Algebra 3.1. Matrix Addition and Multiplication 3.2. Transpose 3.3. Inverse 3.4. Elementary Matrices 3.5. Block Matrices 3.6. Lower and Upper Triangular Matrices and LU Factorization 3.7. Exercises 4. Determinants 4.1. Definition of the Determinant and Properties 4.2. Alternative Definition and Proofs of Properties 4.3. Cramer’s Rule 4.4. Determinants and Volumes 4.5. Exercises 5. Vector Spaces 5.1. Definition of a Vector Space 5.2. Main Examples 5.3. Linear Independence, Span, and Basis 5.4. Coordinate Systems 5.5. Exercises 6. Linear Transformations 6.1. Definition of a Linear Transformation 6.2. Range and Kernel of Linear Transformations 6.3. Matrix Representations of Linear Transformations 6.4. Change of Basis 6.5. Exercises 7. Eigenvectors and Eigenvalues 7.1. Eigenvectors and Eigenvalues 7.2. Similarity and Diagonalizability 7.3. Complex Eigenvalues 7.4. Systems of Differential Equations: the Diagonalizable 7.5. Exercises 8. Orthogonality 8.1. Dot Product and the Euclidean Norm 8.2. Orthogonality and Distance to Subspaces 8.3. Orthonormal Bases and Gram–Schmidt 8.4. Isometries, Unitary Matrices and QR Factorization 8.5. Least Squares Solution and Curve Fitting 8.6. Real Symmetric and Hermitian Matrices 8.7. Singular Value Decomposition 8.8. Exercises Answers to Selected Exercises Appendix A.1. Some Thoughts on Writing Proofs A.1.1. Non-Mathematical Examples A.1.2. Mathematical Examples A.1.3. Truth Tables A.1.4. Quantifiers and Negation of Statements A.1.5. Proof by Induction A.1.6. Some Final Thoughts A.2. Complex Numbers A.3. The Field Axioms Index

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