(*) Suppose that B = T -1AT
and that x is an eigenvector of
A with corresponding
eigenvalue \lambda -- this means that Ax =
\lambda x; A is an n x n
matrix,
x is an n-dimensional column vector and
\lambda is a real (or complex) number.
Show that T -1x is an eigenvector
of B with the same corresponding eigenvalue
\lambda.
This helps explain why, in Long Homework #1, we defined eigenvalues
of matrices in terms
of similar diagonal matrices. It turns out to be equivalent to
the definition in the book.