1st Edition

# Invitation to Linear Algebra

By David C. Mello Copyright 2017
408 Pages 50 B/W Illustrations
by CRC Press

408 Pages 50 B/W Illustrations
by Chapman & Hall

408 Pages 50 B/W Illustrations
by Chapman & Hall

Also available as eBook on:

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.