Practical algorithms for computing
eigenvalues and eigenvectors depend on
manipulating a matrix A in such a way
that the eigenvalues are preserved and
the eigenvectors can be easily recovered
from the new matrix. Okay? Now to that end
we need to introduce the concept of a
similarity transformation. If we have a
matrix, if we have matrices A and B and Y
where Y is non-singular and if B is
equal to Y inverse A times Y then A and
B are said to be similar.  Okay?  And
anytime you hit a matrix with the
inverse on the left and the matrix on
the right, that is known as a similarity
transformation.  And through a sequence of
homeworks, you're going to find out how
similarity transformations fit into the
big picture of eigenvalues and
eigenvectors.
