THIRTY-THREE MINIATURES MATHEMATICAL AND ALGORITHMIC APPLICATIONS OF LINEAR ALGEBRAPDF电子书下载

Miniature 1. Fibonacci Numbers, Quickly 1

Miniature 2. Fibonacci Numbers, the Formula 3

Miniature 3. The Clubs of Oddtown 5

Miniature 4. Same-Size Intersections 7

Miniature 5. Error-Correcting Codes 11

Miniature 6. Odd Distances 17

Miniature 7. Are These Distances Euclidean? 19

Miniature 8. Packing Complete Bipartite Graphs 23

Miniature 9. Equiangular Lines 27

Miniature 10. Where is the Triangle? 31

Miniature 11. Checking Matrix Multiplication 35

Miniature 12. Tiling a Rectangle by Squares 39

Miniature 13. Three Petersens Are Not Enough 41

Miniature 14. Petersen, Hoffman-Singleton, and Maybe 57 45

Miniature 15. Only Two Distances 51

Miniature 16. Covering a Cube Minus One Vertex 55

Miniature 17. Medium-Size Intersection Is Hard To Avoid 57

Miniature 18. On the Difficulty of Reducing the Diameter 61

Miniature 19. The End of the Small Coins 67

Miniature 20. Walking in the Yard 71

Miniature 21. Counting Spanning Trees 77

Miniature 22. In How Many Ways Can a Man Tile a Board? 85

Miniature 23. More Bricks--More Walls? 97

Miniature 24. Perfect Matchings and Determinants 107

Miniature 25. Turning a Ladder Over a Finite Field 113

Miniature 26. Counting Compositions 119

Miniature 27. Is It Associative? 125

Miniature 28. The Secret Agent and the Umbrella 131

Miniature 29. Shannon Capacity of the Union: A Tale of Two Fields 139

Miniature 30. Equilateral Sets 147

Miniature 31. Cutting Cheaply Using Eigenvectors 153

Miniature 32. Rotating the Cube 163

Miniature 33. Set Pairs and Exterior Products 171

Index 179