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Eigenvalues and Eigenvectors Demo

Eigenvalues and Eigenvectors Demo
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2015-03-15 01:47
VectorFunctionCoordinate GeometryGeometric ConstructionSlider Animation
This example demonstrates the geometric significance of eigenvectors and eigenvalues under matrix transformations. It involves core math concepts like eigenvalues, eigenvectors, linear transformations, and matrix operations. Construction highlights include using GeoGebra commands like Intersect, Vector, Textfield, Point, and Segment. Suitable for high school and above students to visually grasp abstract linear algebra concepts.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Vector(O, B) → u
  3. Textfield(a) → inputBox1
  4. Textfield(b) → inputBox2
  5. Textfield(c) → inputBox3
  6. Textfield(d) → inputBox4
  7. Point(v) → C
  8. Segment(C, D) → CoordsVy
  9. Point(CoordsVy) → E
  10. Point(xAxis) → F
  11. Point(CoordsVy) → G
  12. Segment(G, H) → CoordsVx
  13. Segment(B, I) → CoordsUx
  14. Segment(B, J) → CoordsUy

AI Drawing Prompt Reference

Draw a coordinate system with x and y axes, mark the origin, take a point on the x-axis, and draw a vector from the origin to this point. Set four parameters a, b, c, d via input boxes, use these to construct points C and D, connect them to form a line segment, and find intersections with axes to create new points E and F, then connect these points to visualize the geometric significance of eigenvectors and eigenvalues under matrix transformations.
The prompt above was compiled from the original drawing commands and is for reference only.