Elementary Linear Algebra

Elementary Linear Algebra: Applications Version, 12th Edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus.

1 Systems of Linear Equations and Matrices 1

2 Determinants 118

3 Euclidean Vector Spaces 146

4 General Vector Spaces 202

5 Eigenvalues and Eigenvectors 291

6 Inner Product Spaces 341

7 Diagonalization and Quadratic Forms 399

8 General Linear Transformations 446

9 Numerical Methods 509

10 Applications of Linear Algebra 545

Appendix A Working with Proofs A1

Appendix B Complex Numbers A5

Answers To Exercises A12

Index I1