9780135181638

Summary

A thorough and accessible introduction to linear algebra, delivered digitally.
In Linear Algebra with Applications, modern practical application is used to make key concepts tangible and demonstrate how mathematics is used in the real world. Featuring worked examples, exercises, and chapter tests, the text emphasizes the important roles geometry and visualization play in understanding linear algebra.

For sophomore-level or junior/senior-level first courses in linear algebra; assumes calculus as a prerequisite.

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Author Biography

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.

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 Rⁿ

5.2 Orthogonal Subspaces

5.3 Least Squares Problems

5.4 Inner Product Spaces

5.5 Orthonormal Sets

5.6 The Gram–Schmidt 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

Supplemental Materials

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