An Introduction to Linear Algebra 电子书下载
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.- Two Matrices.- 11. Introduction.- 12. Basic nomenclature for matrices.- 13. Addition and subtraction of matrices.- 14. Multiplication of a matrix by a scalar.- 15. 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.- 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.- 27. Generalities about systems of linear equations.- 28. Elementary row operations and systems of linear equations.- Exercises on chapter 3.- 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.- Five Vector Spaces.- 34. Introduction.- 35. The definition of a vector space, and examples.- 36. Elementary consequences of the vector space axioms.- 37. Subspaces.- 38. Spanning sequences.- 39. 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.- 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.- 50. Row- and column-rank of a matrix.- 52. Rank inequalities.- 53. Vector spaces of linear mappings.- Exercises on chapter 6.- Seven Matrices From Linear Mappings.- 54. Introduction.- 55. The main definition and its immediate consequences.- 56. Matrices of sums, etc. of linear mappings.- 56. Matrices of sums, etc. of linear mappings.- 58. Matrix of a linear mapping w.r.t. different bases.- 58. Matrix of a linear mapping w.r.t. different bases.- 60. Vector space isomorphisms.- Exercises on chapter 7.- Eight Eigenvalues, Eigenvectors and Diagonalization.- 61. Introduction.- 62. Characteristic polynomials.- 62. Characteristic polynomials.- 64. Eigenvalues in the case F = ?.- 65. Diagonalization of linear transformations.- 66. Diagonalization of square matrices.- 67. The hermitian conjugate of a complex matrix.- 68. Eigenvalues of special types of matrices.- Exercises on chapter 8.- Nine Euclidean Spaces.- 69. Introduction.- 70. Some elementary results about euclidean spaces.- 71. Orthonormal sequences and bases.- 72. Length-preserving transformations of a euclidean space.- 73. Orthogonal diagonalization of a real symmetric matrix.- Exercises on chapter 9.- Ten Quadratic Forms.- 74. Introduction.- 75. Change ofbasis and change of variable.- 76. Diagonalization of a quadratic form.- 77. Invariants of a quadratic form.- 78. Orthogonal diagonalization of a real quadratic form.- 79. Positive-definite real quadratic forms.- 80. The leading minors theorem.- Exercises on chapter 10.- Appendix Mappings.- Answers to Exercises.
尊敬的读者:
欢迎您访问我们的网站。本站的初衷是为大家提供一个共享学习资料、交换知识的平台。每位用户都可以将文件上传至网盘并分享。
然而,随着用户上传的资料增多,我们发现部分不宜或版权问题的书籍被分享到了本站。
为此,我们已经关闭了分享入口,并进行了多次书籍审查,但仍有部分内容未能彻底审查到位。
在此,我们恳请广大读者与我们共同监督,如发现任何不宜内容,请 点击此处 进行举报,我们会第一时间处理并下架相关内容。
希望我们能共建一个文明社区!感谢您的理解与支持!
猜你喜欢
- 《学会提问:麦肯锡工作法》【日】大岛祥誉, 金磊, 文字版 电子书下载
- 《了不起的古希腊》王冬妮全新修订版 电子书下载
- 《疯语者》玉松鼠文字版 电子书下载
- 《秘密花园》教育部语文新课标必读丛书伯内特文字版 电子书下载
- 《成为自控者:建立幸福人生的正向循环》Susan Kuang文字版 电子书下载
- 《黎明前说我爱你》彼得·加尔多什全译珍藏版 电子书下载
- 《身份危机》汪德嘉经典版 电子书下载
- 《美国家书》富兰克林、洛克菲勒、华盛顿等珍藏版 电子书下载
- 《圣殿春秋》[英] 肯·福莱特 电子书下载
- 《房屋征收拆迁补偿速查速用大全集(案例应用版)》 电子书下载
- 《查理·芒格的智慧:投资的格栅理论(原书第2版)》哈格斯特朗珍藏版 电子书下载
- 《高难度谈话》[美]道格拉斯·斯通 布鲁斯·佩顿 希拉·汉中文版 电子书下载