Invitation to Linear Algebra  book cover
1st Edition

Invitation to Linear Algebra

ISBN 9781498779562
Published April 24, 2017 by Chapman and Hall/CRC
408 Pages 50 B/W Illustrations

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USD $145.00

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Book Description

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.


  • 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

Table of Contents

Matrices and Linear Systems

Introduction to Matrices

Matrix Multiplication

Additional Topics in Matrix Algebra

Introduction to Linear Systems

The Inverse of a Matrix


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


Systems of First Order Differential Equations

Stability Analysis of First Order Systems

Coupled Oscillations


Solutions and Hints to Selected Exercises

View More



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.