Matrix Powers and Eigenvectors: Iterating a Linear Transformation

This GeoGebra example demonstrates how repeated multiplication by a matrix A transforms an initial vector X_0, producing a sequence of vectors whose directions reveal the influence of eigenvectors. It connects matrix powers, eigenvalues λ, eigenvectors, linear transformations, and iterative convergence. The construction uses Sequence to generate the vector sequence, Line and Intersect to define auxiliary directions or intersection points, and objects such as A, X_0, lmbda, n, S, and SL to represent the matrix, starting vector, eigenvalue, iteration count, and sequence or transformed results. Text objects provide labels and explanations. It is suitable for high school linear algebra extensions, introductory college linear algebra, or mathematical visualization activities.