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Linear Algebra, Theory And Applications

Linear algebra , Theory And Applications Kenneth Kuttler September 12, 2017. 2. Contents 1 Preliminaries 11. Sets And Set Notation .. 11. Functions .. 12. The Number Line And algebra Of The Real Numbers .. 12. Ordered fields .. 14. The Complex Numbers .. 15. The Fundamental Theorem Of algebra .. 18. Exercises .. 20. Completeness of R .. 21. Well Ordering And Archimedean Property .. 22. Division .. 24. Systems Of Equations .. 28. Exercises .. 33. Fn .. 34. algebra in Fn .. 34. Exercises .. 35. The Inner Product In Fn .. 35. What Is Linear algebra ? .. 38. Exercises .. 38. 2 Linear Transformations 39. Matrices .. 39. The ij th Entry Of A Product .. 44. Digraphs .. 46. Properties Of Matrix Multiplication .. 48. Finding The Inverse Of A Matrix .. 51. Exercises .. 54. Linear Transformations .. 56. Some Geometrically Defined Linear Transformations .. 58. The Null Space Of A Linear Transformation.

Preface This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra.

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