Coordinate Transformations; The Eigenbasis





Shows that the transformation to the diagonal basis is a rotation of π/4

Which makes sense considering in initialization steps that mymatrix was created with a rotation on π/4 of a diagonal matrix

The next command produces an orthonormal basis of the eigenspace (i.e., the eigenvectors are of unit magnitude):



The command RotationTransform computes a matrix that will rotate vectors ccw about the origin in two dimensions, by a specified angle:



This last result shows that the transformation to the eigenvector space involves rotation by π/4--and that the matrix corresponding to the eigenvectors produces this same transformation

Here is a demonstration of the general result A "index_23.gif" = "index_24.gif" "index_25.gif", where "index_26.gif" is an eigenvector and λ its corresponding eigenvalue:








MatrixPower multiplies a matrix by itself n times…



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