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Further Exploration of Eigenvalues and Eigenvectors

Further Exploration of Eigenvalues and Eigenvectors
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2014-11-14 22:24
VectorCoordinate GeometryMatrix
In collections Linear Algebra
This example demonstrates the concepts of eigenvalues and eigenvectors. It shows how to calculate eigenvalues and eigenvectors and their geometric significance. Commands used include Random, PrimeFactors, RandomElement, GCD, Vector, Length, Point, Determinant, and LaTeX. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Random(-6, 6) → dd
  2. PrimeFactors(abs(bc)) → bopt
  3. RandomElement(bopt) → bb
  4. GCD(abs(Element[QQ, 2, 2] - ev2), abs(Element[QQ, 2, 1])) → ev2gcd
  5. GCD(abs(Element[QQ, 1, 1] - ev1), abs(Element[QQ, 1, 2])) → ev1gcd
  6. Vector((0, 0), (v1x, v1y)) → v1
  7. Length(v1) → lv1
  8. Vector((0, 0), (v2x, v2y)) → v2
  9. Length(v2) → lv2
  10. Point(c) → A
  11. Vector((0, 0), A) → u
  12. Vector((0, 0), B) → v
  13. Determinant(Q) → dq
  14. LaTeX(QQ) → text2