The book focuses on the development of the mathematical theory and also presents many applications to assist instructors and students to master the material and apply it to their areas of interest, whether it be to further their studies in mathematics, science, engineering, statistics, economics, or other disciplines.
The book focuses on the development of the mathematical theory and also presents many applications to assist instructors and students to master the material and apply it to their areas of interest, whether it be to further their studies in mathematics, science, engineering, statistics, economics, or other disciplines.
Hugo J. Woerdeman, PhD, professor, Department of Mathematics, Drexel University, Philadelphia, Pennsylvania, USA, is also the author of Advanced Linear Algebra, published by CRC Press, and a co-author of Matrix Completions, Moments, and Sums of Squares, published by Princeton University Press. He also serves as Vice President of two societies of researchers: The International Linear Algebra Society and The International Workshop on Operator Theory and its Applications.
Inhaltsangabe
Preface to the Instructor Preface to the Student Acknowledgements Notation 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 Spaces, Row Spaces 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. Transpose. Inverse. Elementary Matrices. Block Matrices. Lower and Upper Triangular Matrices and LU Factorization 3.7 Exercises 4.Determinants. Definition of the Determinant and Properties. Alternative Definition and Proofs of Properties. Cramer's rule. Determinants and Volumes. Exercises 5.Vector spaces. Definition of a Vector Space. Main Examples. Linear Independence, Span, and Basis. Coordinate Systems. Exercises. 6.Linear Transformations. Definition of a Linear Transformation. Range and Kernel of Linear Transformations. Matrix Representations of Linear Maps. Change of Basis. Exercises. 7.Eigenvectors and Eigenvalues. Eigenvectors and Eigenvalues. Similarity and Diagonalizability. Complex eigenvalues. Exercises. 8.Orthogonality. Dot Product and the Euclidean Norm. Orthogonality and Distance to Subspaces. Orthonormal Bases and Gram-Schmidt. Unitary Matrices and QR Factorization. Least Squares Solution and Curve Fitting. Real Symmetric and Hermitian Matrices. Appendix.A1.1 Some Thoughts on Writing Proofs. A1.2 Mathematical Examples. A 1.3 Truth Tables. A1.4 Quantifiers and Negation of Statements. A1.5 Proof by Induction. A1.6 Some Final Thoughts. A.2 Complex numbers. A.3 The Field Axioms.
Preface to the Instructor Preface to the Student Acknowledgements Notation 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 Spaces, Row Spaces 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. Transpose. Inverse. Elementary Matrices. Block Matrices. Lower and Upper Triangular Matrices and LU Factorization 3.7 Exercises 4.Determinants. Definition of the Determinant and Properties. Alternative Definition and Proofs of Properties. Cramer's rule. Determinants and Volumes. Exercises 5.Vector spaces. Definition of a Vector Space. Main Examples. Linear Independence, Span, and Basis. Coordinate Systems. Exercises. 6.Linear Transformations. Definition of a Linear Transformation. Range and Kernel of Linear Transformations. Matrix Representations of Linear Maps. Change of Basis. Exercises. 7.Eigenvectors and Eigenvalues. Eigenvectors and Eigenvalues. Similarity and Diagonalizability. Complex eigenvalues. Exercises. 8.Orthogonality. Dot Product and the Euclidean Norm. Orthogonality and Distance to Subspaces. Orthonormal Bases and Gram-Schmidt. Unitary Matrices and QR Factorization. Least Squares Solution and Curve Fitting. Real Symmetric and Hermitian Matrices. Appendix.A1.1 Some Thoughts on Writing Proofs. A1.2 Mathematical Examples. A 1.3 Truth Tables. A1.4 Quantifiers and Negation of Statements. A1.5 Proof by Induction. A1.6 Some Final Thoughts. A.2 Complex numbers. A.3 The Field Axioms.
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