Linear Algebra Essentials
A Comprehensive Introduction to Linear Algebra by Inder K. Rana
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Introduction to Linear Algebra
This comprehensive textbook introduces students to the fundamental concepts of linear algebra, covering key topics such as vector spaces, linear transformations, systems of linear equations, matrices, and applications in various fields.
Key Concepts Covered
- Vector Spaces: definitions, bases, and dimensions
- Linear Transformations: representation by matrices and applications
- Systems of Linear Equations: solving using Gauss Elimination and Row Echelon Form (REF)
- Matrices: operations, properties, and applications
- Applications: computer graphics, differential equations, and Fourier analysis
Features
- Comprehensive Coverage: static and dynamic aspects of linear algebra
- Pedagogical Approach: readings and activities for improved understanding and problem-solving skills
- Practical Applications: relevance to mathematics, science, and engineering students
Table of Contents
1. Introduction to Vector Spaces- Definitions and Examples
- Bases and Dimensions
- Operations on Vector Spaces
2. Linear Transformations
- Introduction to Linear Transformations
- Representation by Matrices
- Applications of Linear Transformations
3. Systems of Linear Equations
- Introduction to Systems of Linear Equations
- Gauss Elimination Method
- Row Echelon Form (REF)
4. Matrices
- Introduction to Matrices
- Operations on Matrices
- Properties of Matrices
5. Applications of Linear Algebra
- Computer Graphics
- Differential Equations
- Fourier Analysis
6. Practical Applications
- Mathematics and Science
- Engineering Applications
- Real-World Examples
7. Conclusion
- Summary of Key Concepts
- Future Directions
- References
8. Appendix
- Glossary of Terms
- Additional Resources
- Index
9. Bibliography
- References
- Recommended Readings
- Online Resources
10. Index
- Subject Index
- Author Index
- Keyword Index
11. About the Author
- Biography
- Publications
- Contact Information
12. About the Publisher
- Company Profile
- Catalog
- Contact Information
Target Audience
Students appearing for mathematics entrance exams and those looking to gain a solid foundation in linear algebra
Key Takeaways
- Comprehensive introduction to linear algebra
- Coverage of key concepts and applications
- Practical examples and exercises for improved understanding