Preface 1. Mathematics and engineers 2. Mappings 3. The nature of generalisation 4. Symbolic conditions for linearity 5. Graphical representation 6. Vectors in a plane 7. Bases 8. Calculations in a vector space 9. Change of axes 10. Specification of a linear mapping 11. Transformations 12. Choice of basis 13. Complex numbers 14. Calculations with complex numbers 15. Complex numbers and trigonometry 16. Trigonometry and exponentials 17. Complex numbers: terminology 19. The logic of complex numbers 20. The algebra of transformations 21. Subtraction of transformations' 22. Matrix notation 23. An application of matrix multiplication 24. An application of linearity 25. procedure for finding invariant lines, eigenvectors and eigenvalues 26. Determinant and inverse 27. Properties of determinants 28. Matrices other than square partitions 29. Subscript and summation notation 30. Row and column vectors 31. Affine and Euclidean geometry 32. Scalar products 33. Transpose quadratic forms 34. Maximum and minimum principles 35. Formal laws of matrix algebra 36. Orthogonal transformations 37. Finding the simplest expressions for quadratic forms 38. Principal axes and eigenvectors 39. Lines, planes and subspaces vector product 40. Null space, column space, row space of a matrix 42. Illustrating the importance of orthogonal matrices 43. Linear programming 44. Linear programming, continued Answers Index.
Preface 1. Mathematics and engineers 2. Mappings 3. The nature of generalisation 4. Symbolic conditions for linearity 5. Graphical representation 6. Vectors in a plane 7. Bases 8. Calculations in a vector space 9. Change of axes 10. Specification of a linear mapping 11. Transformations 12. Choice of basis 13. Complex numbers 14. Calculations with complex numbers 15. Complex numbers and trigonometry 16. Trigonometry and exponentials 17. Complex numbers: terminology 19. The logic of complex numbers 20. The algebra of transformations 21. Subtraction of transformations' 22. Matrix notation 23. An application of matrix multiplication 24. An application of linearity 25. procedure for finding invariant lines, eigenvectors and eigenvalues 26. Determinant and inverse 27. Properties of determinants 28. Matrices other than square partitions 29. Subscript and summation notation 30. Row and column vectors 31. Affine and Euclidean geometry 32. Scalar products 33. Transpose quadratic forms 34. Maximum and minimum principles 35. Formal laws of matrix algebra 36. Orthogonal transformations 37. Finding the simplest expressions for quadratic forms 38. Principal axes and eigenvectors 39. Lines, planes and subspaces vector product 40. Null space, column space, row space of a matrix 42. Illustrating the importance of orthogonal matrices 43. Linear programming 44. Linear programming, continued Answers Index.
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