Power Method for Stochastic Matrices: 7 Iterations

Power Method for Stochastic Matrices: 7 Iterations
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2018-03-08 14:59
This GeoGebra example demonstrates the Power Method applied to a stochastic matrix, showing how a vector converges to the stationary distribution after 7 iterations. Core mathematical concepts include stochastic matrices, matrix multiplication, eigenvalues and eigenvectors, and Markov chain limiting behavior. The construction uses GeoGebra commands such as Intersect, Vector, Point, and Textfield, creating matrix A, initial vector u_0, and iterated vectors u_1 through u_7. Interactive input boxes allow users to modify parameters and observe convergence. Suitable for university linear algebra or numerical analysis courses, and as an advanced high school enrichment to visualize matrix power convergence.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → B
  2. Vector(B, A) → u_0
  3. Point(u_0) → J
  4. Vector(J, F) → u_2
  5. Vector(J, E) → u_1
  6. Vector(J, G) → u_3
  7. Vector(J, H) → u_4
  8. Vector(J, I) → u_5
  9. Textfield(a) → InputBox1
  10. Textfield(b) → InputBox2
  11. Textfield(c) → InputBox3
  12. Textfield(d) → InputBox4