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.
Table of Contents:
1. Matrices andSystems of Equations
1.1 Systems of LinearEquations
1.2 Row Echelon Form
1.3 Matrix Arithmetic
1.4 Matrix Algebra
1.5 ElementaryMatrices
1.6 PartitionedMatrices
MATLAB Exercises
Chapter Test A — Trueor False
Chapter Test B
2. Determinants
2.1 The Determinantof a Matrix
2.2 Properties ofDeterminants
2.3 Additional Topicsand Applications
MATLAB Exercises
Chapter Test A — Trueor False
Chapter Test B
3. Vector Spaces
3.1 Definition andExamples
3.2 Subspaces
3.3 LinearIndependence
3.4 Basis and Dimension
3.5 Change of Basis
3.6 Row Space andColumn Space
MATLAB Exercises
Chapter Test A — Trueor False
Chapter Test B
4. LinearTransformations
4.1 Definition andExamples
4.2 MatrixRepresentations of Linear Transformations
4.3 Similarity
MATLAB Exercises
Chapter Test A — Trueor False
Chapter Test B
5. Orthogonality
5.1 The ScalarProduct in Rn
5.2 OrthogonalSubspaces
5.3 Least SquaresProblems
5.4 Inner ProductSpaces
5.5 Orthonormal Sets
5.6 The Gram–SchmidtOrthogonalization Process
5.7 OrthogonalPolynomials
MATLAB Exercises
Chapter Test A — Trueor False
Chapter Test B
6. Eigenvalues
6.1 Eigenvalues andEigenvectors
6.2 Systems of LinearDifferential Equations
6.3 Diagonalization
6.4 HermitianMatrices
6.5 The SingularValue Decomposition
6.6 Quadratic Forms
6.7 Positive DefiniteMatrices
6.8 NonnegativeMatrices
MATLAB Exercises
Chapter Test A — Trueor False
Chapter Test B
7. Numerical LinearAlgebra
7.1 Floating-PointNumbers
7.2 GaussianElimination
7.3 Pivoting Strategies
7.4 Matrix Norms andCondition Numbers
7.5 OrthogonalTransformations
7.6 The EigenvalueProblem
7.7 Least SquaresProblems
7.8 Iterative Methods
MATLAB Exercises
Chapter Test A — Trueor False
Chapter Test B
8. Canonical Forms
8.1 Nilpotent Operators
8.2 The JordanCanonical Form
Appendix: MATLAB
Bibliography
Answers to SelectedExercises
Index
About the Author :
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 1992–1997.
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.
