ESpaces-LinTransformations.mw

Math 22 Fall 2004

Linear Algebra with Applications


Eigenspaces of a Linear Transformation

November 15, 2004

    Load the packages for doing  Linear Algebra

> with(Student[LinearAlgebra]):

Warning, the protected name `.` has been redefined and unprotected

   Define a matrix that describes a linear trasformation to work with

> A := <<1,1/3>|<1/2,-1/2>>;

A := Matrix([[1, 1/2], [1/3, (-1)/2]])

   Find the eigenvalues

> Eigenvalues(A), evalf(Eigenvalues(A));

Vector[column]([[1/4+1/12*105^(1/2)], [1/4-1/12*105^(1/2)]]), Vector[column]([[1.103912564], [-.6039125641]])

   Apply the transformation to a grid multiple times to see

     the eigenspace corresponding to the largest eigenvalue.

> ApplyLinearTransformPlot( A, grid, iterations = 10, output = animation, scaling=constrained, thickness = 2 );

[Plot]

>