Transcription of Linear Algebra, Theory And Applications
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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 .. 61. Subspaces And Spans.
In the exercises, you may occasionally see "at the beginning. This means you ought to have a look at the exercise above it. Some exercises develop a topic sequentially. There are also a few exercises which appear more than once in the book. I have done this deliberately
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