Do there exist "families" of step-wise canonical transformations, in the sense that:

$${\bf A = TCT}^{-1}, \\{\bf T = T_2}^n$$

So that $${\bf T_2}^k {\bf C} {\bf T_2}^{-k} $$ Also has some canonical structure $\forall k\in\{1,\cdots, n\}$ in some sense similar to $\bf C$.

I realize this question is extremely vague/fuzzy, and I am willing to narrow the question down if either of us can help me do that.

Edit own sandbox example:

Consider the matrices $${\bf T_2}=\left[\begin{array}{cc}1&1\\0&1\end{array}\right] , {\bf C} = \left[\begin{array}{cc}0&a\\0&b\end{array}\right]$$

Now we can verify :

$${\bf T_2}^k{\bf CT_2}^{-k} = \left[\begin{array}{cc}0&a+bk\\0&b\end{array}\right]$$

Basically mimicking a generic linear function (or affine, actually).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.