MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If $A$ is a matrix and $D$ is a diagonal matrix, is there some special name for $DAD$?

share|cite|improve this question
The paternal matrix? ;) – Mark Grant Aug 24 '12 at 12:47
Interesting idea :) – Felix Goldberg Aug 24 '12 at 12:51
$A$ diagonally conjugated by $D$? – Igor Khavkine Aug 24 '12 at 12:52
Or just $A$ conjugated by $D$. – Deane Yang Aug 24 '12 at 13:09
I'd reserve the word "conjugated" for something like $DAD^{-1}$. – Andreas Blass Aug 24 '12 at 14:32
up vote 11 down vote accepted

it is called "diagonal congruence" here. This makes sense, at least when $D$ is real, since it is a congruence. "Conjugate" sounds more like $D^{-1}AD$ or $\overline{A}$ to me.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.