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.

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• Matrices and Systems of Equations  1.1 Systems of Linear Equations 1.2 Row Echelon Form1.3 Matrix Arithmetic1.4 Matrix Algebra1.5 Elementary Matrices1.6 Partitioned MatricesMATLAB ExercisesChapter Test A: True or FalseChapter Test B Determinants 2.1 The Determinant of a Matrix2.2 Properties of Determinants2.3 Additional Topics and ApplicationsMATLAB ExercisesChapter Test A: True or FalseChapter Test B Vector Spaces 3.1 Definition and Examples3.2 Subspaces3.3 Linear Independence3.4 Basis and Dimension3.5 Change of Basis3.6 Row Space and Column SpaceMATLAB ExercisesChapter Test A: True or FalseChapter Test B Linear Transformations 4.1 Definition and Examples4.2 Matrix Representations of Linear Transformations4.3 SimilarityMATLAB ExercisesChapter Test A: True or FalseChapter Test B Orthogonality 5.1 The Scalar Product in Rn5.2 Orthogonal Subspaces5.3 Least Squares Problems5.4 Inner Product Spaces5.5 Orthonormal Sets5.6 The Gram–Schmidt Orthogonalization Process5.7 Orthogonal PolynomialsMATLAB ExercisesChapter Test A: True or FalseChapter Test B Eigenvalues 6.1 Eigenvalues and Eigenvectors6.2 Systems of Linear Differential Equations6.3 Diagonalization6.4 Hermitian Matrices6.5 The Singular Value Decomposition6.6 Quadratic Forms6.7 Positive Definite Matrices6.8 Nonnegative MatricesMATLAB ExercisesChapter Test A: True or FalseChapter Test B Numerical Linear Algebra 7.1 Floating-Point Numbers7.2 Gaussian Elimination7.3 Pivoting Strategies7.4 Matrix Norms and Condition Numbers7.5 Orthogonal Transformations7.6 The Eigenvalue Problem7.7 Least Squares Problems7.8 Iterative MethodsMATLAB ExercisesChapter Test A: True or FalseChapter Test B Canonical Forms 8.1 Nilpotent Operators8.2 The Jordan Canonical FormAppendix: MATLAB Bibliography Answers to Selected Exercises Index

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.

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• Matrices and Systems of Equations  1.1 Systems of Linear Equations 1.2 Row Echelon Form1.3 Matrix Arithmetic1.4 Matrix Algebra1.5 Elementary Matrices1.6 Partitioned MatricesMATLAB ExercisesChapter Test A: True or FalseChapter Test B Determinants 2.1 The Determinant of a Matrix2.2 Properties of Determinants2.3 Additional Topics and ApplicationsMATLAB ExercisesChapter Test A: True or FalseChapter Test B Vector Spaces 3.1 Definition and Examples3.2 Subspaces3.3 Linear Independence3.4 Basis and Dimension3.5 Change of Basis3.6 Row Space and Column SpaceMATLAB ExercisesChapter Test A: True or FalseChapter Test B Linear Transformations 4.1 Definition and Examples4.2 Matrix Representations of Linear Transformations4.3 SimilarityMATLAB ExercisesChapter Test A: True or FalseChapter Test B Orthogonality 5.1 The Scalar Product in Rn5.2 Orthogonal Subspaces5.3 Least Squares Problems5.4 Inner Product Spaces5.5 Orthonormal Sets5.6 The Gram–Schmidt Orthogonalization Process5.7 Orthogonal PolynomialsMATLAB ExercisesChapter Test A: True or FalseChapter Test B Eigenvalues 6.1 Eigenvalues and Eigenvectors6.2 Systems of Linear Differential Equations6.3 Diagonalization6.4 Hermitian Matrices6.5 The Singular Value Decomposition6.6 Quadratic Forms6.7 Positive Definite Matrices6.8 Nonnegative MatricesMATLAB ExercisesChapter Test A: True or FalseChapter Test B Numerical Linear Algebra 7.1 Floating-Point Numbers7.2 Gaussian Elimination7.3 Pivoting Strategies7.4 Matrix Norms and Condition Numbers7.5 Orthogonal Transformations7.6 The Eigenvalue Problem7.7 Least Squares Problems7.8 Iterative MethodsMATLAB ExercisesChapter Test A: True or FalseChapter Test B Canonical Forms 8.1 Nilpotent Operators8.2 The Jordan Canonical FormAppendix: MATLAB Bibliography Answers to Selected Exercises Index