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Matrix Algebra for Engineers by Jeffrey R. Chasnov



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Matrix Algebra for Engineers written by Jeffrey R. Chasnov cover the following topics.

  • 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
  • 2. 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

  • 3. 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

  • 4. 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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