About our authorsSteven 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 [...] 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 [...] 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.

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 GramSchmidtOrthogonalization 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