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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
** Edition: **
** Author(s): ** Jeffrey R Chasnov
** Publisher: **
** Series: **
** Year: **
** Pages: ** 187
** Type: ** PDF
** Language: ** English
** ISBN: **
** 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.
**Part-1 Matrices**

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

Problem Solution

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?2

- Abstract Algebra
- Calculus
- Differential Equations
- Engineering Mathematics
- Linear Algebra
- Math Magic
- Real Analysis

- Basic Algebra
- Basic Mathematics
- Math History
- Math Formulas
- Mathematical Methods
- Number Theory
- Bio Mathematics
- Business Mathematics
- Probability & Statistics

**WORKSHEETS (Solved):- **

**SHORTCUT TRICKS (Division):- **

- Divisible by 2 Shortcut trick
- Divisible by 3 Shortcut trick
- Divisible by 4 Shortcut trick
- Divisible by 5 Shortcut trick
- Divisible by 6 Shortcut trick
- Divisible by 7 Shortcut trick
- Divisible by 8 Shortcut trick
- Divisible by 9 Shortcut trick
- Divisible by 10 Shortcut trick

**SHORTCUT TRICKS (Prime Number):- **

- Find the prime number from 1 to 100 just in 5 second (MATH PRIME NUMBER SHORTCUT TRICK from 1 to 100 number) ?
- Find a large number "A" is prime number or not (MATH PRIME NUMBER SHORTCUT TRICK By using Square Root method) ?
- Find the composite number from 1 to 100 just in 5 second (MATH COMPOSITE NUMBER SHORTCUT TRICK from 1 to 100 number) ?