Published by Pearson (November 25, 2020) © 2021
Steven Leon | Lisette de PillisThis 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.
The full text downloaded to your computer
With eBooks you can:
- search for key concepts, words and phrases
- make highlights and notes as you study
- share your notes with friends
eBooks are downloaded to your computer and accessible either offline through the Bookshelf (available as a free download), available online and also via the iPad and Android apps.
Upon purchase, you'll gain instant access to this eBook.
Time limit
The eBooks products do not have an expiry date. You will continue to access your digital ebook products whilst you have your Bookshelf installed.
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