This book presents the basic ideas of linear algebra in a manner that users will find understandable. It offers a fine balance between abstraction/theory and computational skills, and gives readers an excellent opportunity to learn how to handle abstract concepts. Included in this comprehensive and easy-to-follow manual are these topics: linear equations and matrices; solving linear systems; real vector spaces; inner product spaces; linear transformations and matrices; determinants; eigenvalues and eigenvectors; differential equations; and MATLAB for linear algebra. Because this book gives real applications for linear algebraic basic ideas and computational techniques, it is useful as a reference work for mathematicians and those in field of computer science.

1. Linear Equations and Martices 2. Solving Linear Systems 3. Real Vector Spaces 4. Inner Product Spaces 5. Linear Transformations and Martices 6. Determinants 7. Eigenvalues and Eigenvectors 8. Differential Equations(Optional) 9. Matlab for Linear Algebra 10. Matlab Exercises Appendix A: Preliminaries Appendix B: Complex Numbers Appendix C: Introduction to Proofs Answers to Odd-Numbered Exercises

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