Linear Algebra with Applications, Global Edition

10. Auflage 2021
ISBN: 978-1-292-35486-6
Verlag: Pearson Education Limited

Buch, Englisch, 560 Seiten, Format (B × H): 200 mm x 250 mm, Gewicht: 956 g

This book is for junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite.

This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualisation play in understanding linear algebra.

Autoren/Hrsg.

Leon, Steven

de Pillis, Lisette

Inhaltsverzeichnis

1. Matrices and Systems of Equations
   • 1.1 Systems of Linear Equations
   • 1.2 Row Echelon Form
   • 1.3 Matrix Arithmetic
   • 1.4 Matrix Algebra
   • 1.5 Elementary Matrices
   • 1.6 Partitioned Matrices
   • MATLAB Exercises
   • Chapter Test A: True or False
   • Chapter Test B
2. Determinants
   • 2.1 The Determinant of a Matrix
   • 2.2 Properties of Determinants
   • 2.3 Additional Topics and Applications
   • MATLAB Exercises
   • Chapter Test A: True or False
   • Chapter Test B
3. Vector Spaces
   • 3.1 Definition and Examples
   • 3.2 Subspaces
   • 3.3 Linear Independence
   • 3.4 Basis and Dimension
   • 3.5 Change of Basis
   • 3.6 Row Space and Column Space
   • MATLAB Exercises
   • Chapter Test A: True or False
   • Chapter Test B
4. Linear Transformations
   • 4.1 Definition and Examples
   • 4.2 Matrix Representations of Linear Transformations
   • 4.3 Similarity
   • MATLAB Exercises
   • Chapter Test A: True or False
   • Chapter Test B
5. Orthogonality
   • 5.1 The Scalar Product in R
   • 5.2 Orthogonal Subspaces
   • 5.3 Least Squares Problems
   • 5.4 Inner Product Spaces
   • 5.5 Orthonormal Sets
   • 5.6 The GramSchmidt Orthogonalization Process
   • 5.7 Orthogonal Polynomials
   • MATLAB Exercises
   • Chapter Test A: True or False
   • Chapter Test B
6. Eigenvalues
   • 6.1 Eigenvalues and Eigenvectors
   • 6.2 Systems of Linear Differential Equations
   • 6.3 Diagonalization
   • 6.4 Hermitian Matrices
   • 6.5 The Singular Value Decomposition
   • 6.6 Quadratic Forms
   • 6.7 Positive Definite Matrices
   • 6.8 Nonnegative Matrices
   • MATLAB Exercises
   • Chapter Test A: True or False
   • Chapter Test B
7. Numerical Linear Algebra
   • 7.1 Floating-Point Numbers
   • 7.2 Gaussian Elimination
   • 7.3 Pivoting Strategies
   • 7.4 Matrix Norms and Condition Numbers
   • 7.5 Orthogonal Transformations
   • 7.6 The Eigenvalue Problem
   • 7.7 Least Squares Problems
   • 7.8 Iterative Methods
   • MATLAB Exercises
   • Chapter Test A: True or False
   • Chapter Test B
8. Canonical Forms
   • 8.1 Nilpotent Operators
   • 8.2 The Jordan Canonical Form
   Appendix: MATLAB Bibliography Answers to Selected Exercises Index

Über Autor(innen)

About our authors

Steven J. Leon is a Chancellor Professor Emeritus at the University of Massachusetts Dartmouth. He has been a Visiting Professor at Stanford University, ETH Zurich (the Swiss Federal Institute of Technology), KTH (the Royal Institute of Technology in Stockholm), UC San Diego, and Brown University. His areas of specialty are linear algebra and numerical analysis.

Leon has been active in the International Linear Algebra Society (ILAS). He served as Editor-in-Chief of Image, the Bulletin of the International Linear Algebra Society from 1989 to 1997. He also served two terms as Chair of the ILAS Education Committee. In the 1990's he served as Director of the NSF sponsored ATLAST Project (Augmenting the Teaching of Linear Algebra using Software Tools). The project conducted 18 regional faculty workshops during the period from 19921997.

Professor Leon is now living in San Diego, where he remains professionally active and participates in the Computational Mathematics seminars at UCSD.

Lisette de Pillis holds the Norman F. Sprague chaired Professorship in the Life Sciences, and is department chair and a professor of mathematics at Harvey Mudd College. De Pillis has also been the director of the Harvey Mudd College Global Clinic Program and the Director for the Center for Quantitative Life Sciences.

De Pillis is a Fellow of the American Mathematical Society, an Argonne National Laboratory Maria Goeppert-Mayer Distinguished Scholar, and a HERS-CBL Clare Booth Luce Leadership in STEM Scholar. She has been an officer of the Society for Mathematical Biology, a guest editor for the MAA American Mathematical Monthly, an Editorial Board Member for the AMS Notices, Associate Editor for the Undergraduate Mathematics Applications Project, and a Board Member for Springer Undergraduate Texts in Mathematics.