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PLU Decomposition of a Matrix

PLU Decomposition of a Matrix
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2013-03-03 19:28
Coordinate GeometryMatrixTransformation
This example demonstrates the PLU decomposition of a matrix A, where P is a permutation matrix, L is a lower triangular matrix, and U is an upper triangular matrix. Using GeoGebra commands like Random, Transpose, etc., the dynamic process of matrix transformation is shown. Suitable for high school and above students to learn matrix theory.

GeoGebra Commands & Parameters

  1. Random(-5, 5) → A6
  2. Random(-5, 5) → B6
  3. Random(-5, 5) → C6
  4. Random(-5, 5) → A7
  5. Random(-5, 5) → B7
  6. Random(-5, 5) → C7
  7. Random(-5, 5) → A8
  8. Random(-5, 5) → B8
  9. Random(-5, 5) → C8
  10. Transpose({Sequence[abs(Element[A, i, 1]), i, 1, 3]}) → list2
  11. Reverse(Sort[Sequence[(Element[list2, i, 1], i), i, 1, 3]]) → c
  12. If(abs(Element[U_0, 1, 1]) ≟ Element[x(c), 1], {1, 2, 3}, list7) → list8
  13. Sequence(Element[A, Element[list8, i]], i, 1, 3) → U_1
  14. Sequence(abs(Element[U_2, i, 2]), i, 2, 3) → list13
  15. Max(list13) → g
  16. Sequence(Element[list2, i, 1], i, 1, 3) → list10
  17. Max(list10) → e
  18. IndexOf(e, list10) → f
  19. Sequence(If[i ≟ f, 1, i], i, 2, 3) → list11
  20. Append(f, list11) → list12
  21. Transpose({Sequence[abs(Element[U_2, i, 2]), i, 2, 3]}) → list3
  22. Reverse(Sort[Sequence[(Element[list3, i, 1], i + 1), i, 1, 2]]) → list4
  23. Append(1, y(list4)) → list5
  24. If(abs(Element[U_2, 2, 2]) ≟ Element[x(list4), 1], {1, 2, 3}, list5) → list9
  25. Random(-5, 5) → C8_1
  26. Random(-5, 5) → B8_1
  27. Random(-5, 5) → A8_1
  28. Random(-5, 5) → C7_1
  29. Random(-5, 5) → B7_1
  30. Random(-5, 5) → A7_1
  31. Random(-5, 5) → C6_1
  32. Random(-5, 5) → B6_1
  33. Random(-5, 5) → A6_1
  34. Random(-5, 5) → C8_2
  35. Random(-5, 5) → B8_2
  36. Random(-5, 5) → A8_2
  37. Random(-5, 5) → C7_2
  38. Random(-5, 5) → B7_2
  39. Random(-5, 5) → A7_2
  40. Random(-5, 5) → C6_2
  41. Random(-5, 5) → B6_2
  42. Random(-5, 5) → A6_2
  43. Determinant(P_0) → D_1
  44. Sequence(Element[P_0, Element[list12, i]], i, 1, 3) → P_1
  45. Transpose({Sequence[abs(Element[U_1, i, 1]), i, 1, 3]}) → matrix1
  46. Sequence(Element[I, Element[list5, i], 1], i, 1, 2) → list6
  47. Sequence(Element[P_1, Element[list5, i]], i, 1, 3) → P_2
  48. Sequence(Element[I, Element[list14, i]], i, 1, 3) → Ptemp
  49. Element(list1, 1) → a
  50. Element(U_0, 1, 1) → b
  51. Element(c, 1) → B
  52. Element(x(c), 1) → d

AI Drawing Prompt Reference

Draw a 3x3 matrix A and perform PLU decomposition to generate matrices P, L, and U. First, randomly generate the elements of matrix A, then calculate matrix P, followed by matrices L and U, and finally show the decomposition process.
The prompt above was compiled from the original drawing commands and is for reference only.