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二维和一维特征空间

二维和一维特征空间
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2019-04-26 04:30
向量解析几何矩阵
所属专题 Linear Algebra with Applications-Interactive Demonstrations
这个范例演示了二维和一维特征空间的概念。通过矩阵变换，展示了特征向量和特征值的几何意义。使用了ApplyMatrix, Sequence等命令，适合高中数学教学。

GeoGebra 命令及参数

  1. ApplyMatrix(M, e_{1}) → t_{1}
  2. ApplyMatrix(M, e_{2}) → t_{2}
  3. ApplyMatrix(M, e_{3}) → t_{3}
  4. Sequence(Sequence[Sequence[(x_{1}, x_{2}, x_{3}), x_{1}, -4, 4, 1], x_{2}, -4, 4, 1], x_{3}, -4, 4, 1) → l1
  5. ApplyMatrix(M, l1) → l1'
  6. ApplyMatrix(M, x_{1}) → u
  7. ApplyMatrix(M, x_{2}) → v
  8. ApplyMatrix(M, x_{3}) → w
  9. Sequence(ApplyMatrix[M, (t, t, t)], t, -5, 5, 0.2) → l2
  10. Sequence(Sequence[Point[(0, 0, 0), Vector[(m * v) + (n * w)]], m, -5, 5], n, -5, 5) → l5
  11. ApplyMatrix(M, l5) → l5'