Linear Algebra with Applications is an introductory text targeted to second or advanced first year undergraduates in engineering or mathematics. The organization of this textis motivated by the authors' experience which tells them what essential concepts should be mastered by students in a one semester undergraduate Linear Algebra course.The authors' main objectives are to fully develop each topic before moving on and to connect topics naturally. The authors take great care to meet both these objectives, because this organization will allow instructors teaching from this text to stay on task so that each topic can be covered with the depth required before progressing to the next logical one. As a result the reader is prepared for each new unit and there is no need to repeat a concept in a subsequent chapter when it is utilized. This text is geared towards an introductory linear algebra course taken by first or second year undergraduate students. However, it offers the opportunity to introduce the importance of abstraction, not only in mathematics, but in many other areas where Linear Algebra is used. The textbook’s approach is to take advantage of this opportunity by presenting abstract vector spaces as early as possible. Throughout the text, the authors are mindful of the difficulties that students at this level have with abstraction and introduce new conceptsfirst through examples which gently illustrate the idea. To motivate the definition of an abstract vector space, and the subtle concept of linear independence, the authors use addition and scalar multiplication of vectors in Euclidean Space. The authors have strived to create a balance between computation, problem solving, and abstraction. This approach equips students with the necessary skills and problem solving strategies in an abstract setting that allows for a greater understanding and appreciation for the numerous applications of the subject.

Table of Contents:
Introduction to Linear Algebra, Defranza & Gigliardi Chapter1 Systems of Linear Equations and Matrices 1-1.1 Systems of Linear Equations Exercise Set 1.1 -1.2 Matrices and Elementary Row Operations Exercise Set 1.2 -1.3 Matrix Algebra Exercise Set 1.3 -1.4 The Inverse of a Square Matrix Exercise Set 1.4 -1.5 Matrix Equations Exercise Set 1.5 -1.6 Determinants Exercise Set 1.6 -1.7 Elementary Matrices and LU Factorization Exercise Set 1.7 -1.8 Applications of Systems of Linear Equatio Exercise Set 1.8 Review Exercises Chapter Test Chapter2 Linear Combinations and Linear Independence-2.1 Vectors in Rn Exercise Set 2.1 -2.2 Linear Combinations Exercise Set 2.2 -2.3 Linear Independence Exercise Set 2.3 Review Exercises Chapter Test Chapter3 Vector Spaces-3.1 Definition of a Vector Space Exercise Set 3.1 -3.2 Subspaces Exercise Set 3.2 -3.3 Basis and Dimension Exercise Set 3.3 -3.4 Coordinates and Change of Basis Exercise Set 3.4 -3.5 Application : Differential Equations Exercise Set 3.5 Review Exercises Chapter Test Chapter4 Linear Transformations -4.1 Linear Transformations Exercise Set 4.1 -4.2 The Null Space and Range Exercise Set 4.2 -4.3 Isomorphisms Exercise Set 4.3 -4.4 Matrix Representation of a Linear Transformation Exercise Set 4.4 -4.5 Similarity Exercise Set 4.5 -4.6 Application : Computer Graphics Exercise Set 4.6 Review Exercises Chapter Test Chapter5 Eigenvalues and Eigenvectors-5.1 Eigenvalues and Eigenvectors Exercise Set 5.1 -5.2 Diagonalization Exercise Set 5.2 -5.3 Application : Systems of Linear Different Exercise Set 5.3 -5.4 Application : Markov Chains Exercise Set 5.4 Review Exercises Chapter Test Chapter6 Inner Product Spaces-6.1 The Dot Product on Rn Exercise Set 6.1 -6.2 Inner Product Spaces Exercise Set 6.2 -6.3 Orthonormal Bases Exercise Set 6.3 -6.4 Orthogonal Complements Exercise Set 6.4 -6.5 Application : Least Squares Approximation Exercise Set 6.5 -6.6 Diagonalization of Symmetric Matrices Exercise Set 6.6 -6.7 Application : Quadratic Forms Exercise Set 6.7 -6.8 Application : Singular Value Decomposition Exercise Set 6.8 Review Exer