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Eigenvalue-Eigenvector Visualization

Eigenvalue-Eigenvector Visualization
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2014-11-29 00:17
VectorMatrixTransformation
This example visualizes the concepts of eigenvalues and eigenvectors. By inputting a matrix, you can see how eigenvectors change under matrix transformation. Commands used: Textfield, Circle, Point, Vector; Objects: d, c, a, b, matrix1, inputBox1, inputBox2, inputBox3, inputBox4, e, v, X_1, Av, AX, p, E, x2_1, text1, f, g. Suitable for linear algebra courses.

GeoGebra Commands & Parameters

  1. Textfield(a) → inputBox1
  2. Textfield(b) → inputBox2
  3. Textfield(c) → inputBox3
  4. Textfield(d) → inputBox4
  5. Circle((0, 0), 1) → e
  6. Point(e) → v
  7. Vector((0, 0), v) → X_1
  8. Vector((0, 0), Av) → AX

AI Drawing Prompt Reference

Draw a unit circle and select a point on it as an eigenvector. Then, input the four elements of a matrix to calculate its transformation under the matrix, and display the resulting vector.
The prompt above was compiled from the original drawing commands and is for reference only.