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BL
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| Record Number
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844940
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| Main Entry
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Whitelaw, Thomas A.
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| Title & Author
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Introduction to Linear Algebra /\ Thomas A. Whitelaw.
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| Edition Statement
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2nd edition.
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| Publication Statement
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Abingdon, Oxon ;New York, NY :: Routledge,, 2018.
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| Page. NO
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1 online resource (286 pages)
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| ISBN
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0203750020
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: 1351436856
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: 9780203750025
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: 9781351436854
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113840215X
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9780751401592
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9781138402157
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| Notes
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65. Diagonalization of linear transformations
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| Contents
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Cover; Half Title; Title Page; Copyright Page; Preface; Table of Contents; Chapter One: A SYSTEM OF VECTORS; 1. Introduction; 2. Description of the system E3; 3. Directed line segments and position vectors; 4. Addition and subtraction of vectors; 5. Multiplication of a vector by a scalar; 6. Section formula and collinear points; 7. Centroids of a triangle and a tetrahedron; 8. Coordinates and components; 9. Scalar products; 10. Postscript; Exercises on chapter 1; Chapter Two: MATRICES; 11. Introduction; 12. Basic nomenclature for matrices; 13. Addition and subtraction of matrices
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14. Multiplication of a matrix by a scalar15. Multiplication of matrices; 16. Properties and non-properties of matrix multiplication; 17. Some special matrices and types of matrices; 18. Transpose of a matrix; 19. First considerations of matrix inverses; 20. Properties of nonsingular matrices; 21. Partitioned matrices; Exercises on chapter 2; Chapter Three: ELEMENTARY ROW OPERATIONS; 22. Introduction; 23. Some generalities concerning elementary row operations; 24. Echelon matrices and reduced echelon matrices; 25. Elementary matrices; 26. Major new insights on matrix inverses
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27. Generalities about systems of linear equations28. Elementary row operations and systems of linear equations; Exercises on chapter 3; Chapter Four: AN INTRODUCTION TO DETERMINANTS; 29. Preface to the chapter; 30. Minors, cofactors, and larger determinants; 31. Basic properties of determinants; 32. The multiplicative property of determinants; 33. Another method for inverting a nonsingular matrix; Exercises on chapter 4; Chapter Five: VECTOR SPACES; 34. Introduction; 35. The definition of a vector space, and examples; 36. Elementary consequences of the vector space axioms; 37. Subspaces
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38. Spanning sequences39. Linear dependence and independence; 40. Bases and dimension; 41. Further theorems about bases and dimension; 42. Sums of subspaces; 43. Direct sums of subspaces; Exercises on chapter 5; Chapter Six: LINEAR MAPPINGS; 44. Introduction; 45. Some examples of linear mappings; 46. Some elementary facts about linear mappings; 47. New linear mappings from old; 48. Image space and kernel of a linear mapping; 49. Rank and nullity; 50. Row- and column-rank of a matrix; 51. Systems of linear equations revisited; 52. Rank inequalities; 53. Vector spaces of linear mappings
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Exercises on chapter 6Chapter Seven: MATRICES FROM LINEAR MAPPINGS; 54. Introduction; 55. The main definition and its immediate consequences; 56. Matrices of sums, etc. of linear mappings; 57. Change of basis; 58. Matrix of a linear mapping w.r.t. different bases; 59. The simplest matrix representing a linear mapping; 60. Vector space isomorphisms; Exercises on chapter 7; Chapter Eight: EIGENVALUES, EIGENVECTORS AND DIAGONALIZATION; 61. Introduction; 62. Characteristic polynomials; 63. Eigenvalues and eigenvectors; 64. Eigenvalues in the case F = C
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| Subject
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Algebras, Linear.
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| Subject
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Algebras, Linear.
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| Subject
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MATHEMATICS-- Algebra-- Intermediate.
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| Dewey Classification
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512/.5
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| LC Classification
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QA184.W485 2018
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