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矩阵相关空间

矩阵相关空间
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2017-02-24 08:04
向量解析几何矩阵
所属专题 Linear Algebra
①本范例演示矩阵的零空间、像空间及相关几何表示；②涉及核心数学概念包括矩阵秩、线性无关基、线性变换；③构造中运用了Random, Sequence, Sort, ReducedRowEchelonForm, Identity, Remove, Transpose等GeoGebra命令；④适合高中及以上学生及线性代数初学者学习矩阵空间理论。

GeoGebra 命令及参数

  1. Random(1, 3) → nullity
  2. Random(2, 4) → s
  3. Sequence(i, i, 1, n) → olist
  4. Sort(Take[Shuffle[olist], n - s + 1]) → olistcut
  5. Sequence(Sequence[If[i ≟ Element[olistcut, j], 1, i > Element[olistcut, j], Random[-5, 5], 0], i, 1, n], j, 1, n) → ns
  6. ReducedRowEchelonForm(ns) → rrofns
  7. Random(1, nullity) → npad
  8. Random(1, nrow) → s2
  9. Random(1, nrow) → s1
  10. Sequence(Sequence[If[(i ≟ j ∧ i ≟ s1 ∨ i ≟ j ∧ i ≟ s2) ∧ (s1 ≠ s2), -1, 0], i, 1, nrow], j, 1, nrow) → swaptozero
  11. Sequence(Sequence[If[i ≟ s1 ∧ j ≟ s2 ∨ i ≟ s2 ∧ j ≟ s1, 1, If[i ≟ j, 1, 0]], i, 1, nrow], j, 1, nrow) → startswap
  12. Sequence(Sequence[Element[rrofns, i, j], j, 1, n], i, 1, s + npad) → notsquare
  13. Sequence(Sequence[If[i > j, Random[-5, 5], 0], i, 1, s + npad], j, 1, s + npad) → t5
  14. Sequence(Sequence[If[i < j, Random[-5, 5], 0], i, 1, s + npad], j, 1, s + npad) → t6
  15. Identity(s + npad) → idenpad
  16. Remove(olist, olistcut) → par
  17. Sequence(Sequence[If[i ≟ Element[par, j], 1, IndexOf[i, par]^(2) > 0, 0, (-Element[rrofns, IndexOf[i, olistcut], Element[par, j]])], i, 1, n], j, 1, n - s) → basisnull
  18. Sequence(Sequence[Element[rrofns, i, j], j, 1, n], i, 1, s) → rightsize
  19. Identity(s) → iden
  20. Sequence(Sequence[If[i < j, Random[-5, 5], 0], i, 1, s], j, 1, s) → t1
  21. Sequence(Sequence[If[i > j, Random[-5, 5], 0], i, 1, s], j, 1, s) → t2
  22. ReducedRowEchelonForm(togive) → togivecheck
  23. Transpose(togivenotsquare) → transposespace
  24. ReducedRowEchelonForm(transposespace) → transposespacerref
  25. Sequence(Sequence[If[i < j, Random[-5, 5], 0], i, 1, n], j, 1, n) → t3
  26. Identity(n) → idenn
  27. Sequence(Sequence[If[i > j, Random[-5, 5], 0], i, 1, n], j, 1, n) → t4
  28. ReducedRowEchelonForm(togivesquare) → togivesquarecheck
  29. Transpose(togivesquare) → transposetogivesquare
  30. ReducedRowEchelonForm(transposetogivesquare) → transpsquaretogive
  31. ReducedRowEchelonForm(togivenotsquare) → togivenotsquarecheck