Matrix Algebra for Engineers by Jeffrey R Chasnov
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About this book :-
Matrix Algebra for Engineers written by
Jeffrey R Chasnov .
There are problems at the end of each lecture chapter and author has tried to choose problems that exemplify the main idea of the lecture. Students taking a formal university course in matrix or linear algebra will usually be assigned many more additional problems, but here author follow the philosophy that less is more. Author give enough problems for students to solidify their understanding of the material, but not too many problems that students feel overwhelmed and drop out. Author do encourage students to attempt the given problems, but if they get stuck, full solutions can be found in the Appendix.
There are also additional problems at the end of coherent sections that are given as practice quizzes on the Coursera platform. Again, students should attempt these quizzes on the platform, but if a student has trouble obtaining a correct answer, full solutions are also found in the Appendix.
The mathematics in this matrix algebra course is at the level of an advanced high school student, but typically students would take this course after completing a university-level single variable calculus course. There are no derivatives and integrals in this course, but student’s are expected to have a certain level of mathematical maturity. Nevertheless, anyone who wants to learn the basics of matrix algebra is welcome to join.
(Jeffrey R Chasnov)
Book Detail :-
Title: Matrix Algebra for Engineers
Author(s): Jeffrey R Chasnov
Country: Hong Kong
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About Author :-
Author Jeffrey R. Chasnov is a Professor of Mathematics at the Hong Kong University of Science and Technology, where he has been teaching since 1993. He is an expatriate American from New York and California, and earned his BA from UC Berkeley and PhD from Columbia University, with post-doctoral fellowships at NASA, Stanford, and Grenoble, France, and a sabbatical semester at Harvey Mudd College. He is the author of numerous research articles in fluid turbulence and mathematical biology, and has authored online textbooks and videos for his courses on differential equations, matrix algebra, mathematical biology and scientific computation. Before and after work, he enjoys family life, swimming and tennis, and takes great pleasure in his family’s annual camping and skiing vacations.
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Book Contents :-
Matrix Algebra for Engineers written by
Jeffrey R Chasnov
cover the following topics.
1. Definition of a matrix
2. Addition and multiplication of matrices
3. Special matrices
4. Transpose matrix
5. Inner and outer products
6. Inverse matrix
7. Orthogonal matrices
8. Orthogonal matrices example
9. Permutation matrices
Part-II Systems of linear equations
10. Gaussian elimination
11. Reduced row echelon form
12. Computing inverses
13. Elementary matrices
14. LU decomposition
15. Solving (LU)x = b
Part-III Vector spaces
16. Vector spaces
17. Linear independence
18. Span, basis and dimension
19. Gram-Schmidt process
20. Gram-Schmidt process example
21. Null space
22. Application of the null space
23. Column space
24. Row space, left null space and rank
25. Orthogonal projections
26. The least-squares problem
27. Solution of the least-squares problem
Part-IV Eigenvalues and eigenvectors
28. Two-by-two and three-by-three determinants
29. Laplace expansion
30. Leibniz formula
31. Properties of a determinant
32. The eigenvalue problem
33. Finding eigenvalues and eigenvectors (1)
34. Finding eigenvalues and eigenvectors (2)
35. Matrix diagonalization
36. Matrix diagonalization example
37. Powers of a matrix
38. Powers of a matrix example
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