Invitation to Linear Algebra is an informative, clearly written, flexible textbook for instructors and students.
Based on over 30 years of experience as a mathematics professor, the author invites students to develop a more informed understanding of complex algebraic concepts using innovative, easy-to-follow methods.
The book is organized into lessons rather than chapters. This limits the size of the mathematical morsels that students must digest, making it easier for instructors to budget class time.
Each definition is carefully explained with detailed proofs of key theorems, including motivation for each step. This makes the book more flexible, allowing instructors to choose material that reflects their and their students’ interests.
A larger than normal amount of exercises illustrate how linear and nonlinear algebra apply in the students’ areas of study.
Features
- The book’s unique lesson format enables students to better understand algebraic concepts
- Students will learn key elements of linear algebra in an enjoyable fashion
- Large number of exercises illustrate the applications of the course material
- Allows instructors to create a course around individual lessons
- Detailed solutions and hints are provided to selected exercises
Matrices and Linear Systems
Introduction to Matrices
Matrix Multiplication
Additional Topics in Matrix Algebra
Introduction to Linear Systems
The Inverse of a Matrix
Determinants
Introduction to Determinants
Properties of Determinants
Applications of Determinants
A First Look at Vector Spaces
Introduction to Vector Spaces
Subspaces of Vector Spaces
Linear Dependence and Independence
Basis and Dimension
The Rank of a Matrix
Linear Systems Revisited
More About Vector Spaces
Sums and Direct Sums of Subspaces
Quotient Spaces
Change of Basis
Euclidean Spaces
Orthonormal Bases
Linear Transformations
Introduction to Linear Transformations
Isomorphisms of Vector Spaces
The Kernel and Range of a Linear Transformation
Matrices of Linear Transformations
Similar Matrices
Matrix Diagonalization
Eigenvalues and Eigenvectors
Diagonalization of Square Matrices
Diagonalization of Symmetric Matrices
Complex Vector Spaces
Complex Vector Spaces
Unitary and Hermitian Matrices
Advanced Topics
Powers of Matrices
Functions of a Square Matrix
Matrix Power Series
Minimal Polynomials
Direct Sum Decompositions
Jordan Canonical Form
Applications
Systems of First Order Differential Equations
Stability Analysis of First Order Systems
Coupled Oscillations
Appendix
Solutions and Hints to Selected Exercises
Biography
David C. Mello received an M.A. degree in Mathematics from Rhode Island College, and both M.S. and Ph.D. degrees in Applied Mathematics from Brown University. He is currently Professor of Mathematics, Department of Mathematics, Johnson & Wales University, Providence, Rhode Island. He has taught college-level mathematics for more than 30 years.
