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Eigenvalue/Eigenvector

Eigenvalue/Eigenvector
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2014-11-07 04:18
VectorMatrixTransformationGeometric Construction
In collections Linear Algebra
This example demonstrates finding the eigenvalue and eigenvector of a 2x2 matrix with visualization options. Key mathematical concepts include matrix operations, eigenvalue solving, and linear transformations. Construction involves GeoGebra commands such as RandomElement, Vector, Length, Point, Determinant, etc. Suitable for high school or undergraduate students learning linear algebra and matrix transformations.

GeoGebra Commands & Parameters

  1. RandomElement({-2, 2}) → v1x
  2. Vector((0, 0), (v1x, v1y)) → v1
  3. Length(v1) → lv1
  4. Vector((0, 0), (v2x, v2y)) → v2
  5. Length(v2) → lv2
  6. Point(c) → A
  7. Vector((0, 0), A) → u
  8. Vector((0, 0), B) → v
  9. Determinant(Q) → dq
  10. LaTeX(P) → text2

AI Drawing Prompt Reference

Visualize a 2D linear transformation with randomly generated vectors, showing their lengths, and display the path of a point under the transformation. Include the determinant of the matrix and label key mathematical concepts.
The prompt above was compiled from the original drawing commands and is for reference only.