Timeline for Normalizing a matrix via triangular transformations

6 events

when toggle format	what		by	license	comment
Jan 25, 2015 at 14:30	history	edited	Ludwig	CC BY-SA 3.0	added 248 characters in body
Jan 25, 2015 at 2:21	answer	added	Tadashi		timeline score: 1
Jan 21, 2015 at 10:05	history	edited	Ludwig	CC BY-SA 3.0	deleted 39 characters in body
Jan 21, 2015 at 10:05	comment	added	Ludwig		You are absolutely right. Anyway, my main concern is to find (if there exists) a triangular similarity transformation which normalizes $A$. Now, if we restrict the attention to the subclass of normal matrices which are circulant, this is not possible (for every choice of the parameters). But what can be said about the general case? (I edit the question accordingly.)
Jan 21, 2015 at 1:03	comment	added	David Handelman		If you assume that $T$ also has to be real, and that such a $T$ exists for every choice of $\alpha_i, \beta_i, \gamma_i$, then for $n=2$, and likely for all $n$, this is impossible. A real circulant matrix has to have a real eigenvalue, and we can certainly choose the entries to have no real eigenvalues when $n=2$, and presumably for every $n$ (I didn't bother checking). Maybe the question is supposed to be, if for a fixed choice of entries, $A$ is conjugate to a circulant matrix, then can we say what $T$ would look like?
Jan 20, 2015 at 21:35	history	asked	Ludwig	CC BY-SA 3.0