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2D and 1D Eigenspaces by Dr. Ian Lundholm

2D and 1D Eigenspaces by Dr. Ian Lundholm
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2019-04-26 04:30
VectorCoordinate GeometryMatrix
In collections Linear Algebra with Applications-Interactive Demonstrations
This example illustrates the concepts of 2D and 1D eigenspaces. Through matrix transformations, it demonstrates the geometric meaning of eigenvectors and eigenvalues. Commands like ApplyMatrix and Sequence are used, suitable for high school math education.

GeoGebra Commands & Parameters

  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'