How do you solve :$$AX+BXC=D$$ for $X$ where all of them are 2by 2 matrices?
Asked
Active
Viewed 29 times
0
-
See homework. See also this post and related ones. – Dietrich Burde Apr 18 '20 at 18:50
-
What are your thoughts on the problem? What have you tried? Where are you getting stuck? – Ben Grossmann Apr 18 '20 at 19:03
-
I know it is related to Sylvester equation, I want to fist understand Sylvester equation, I.e when does it have roots. And then I want to know how it is related to Sylvester equation. – user 6663629 Apr 18 '20 at 19:05
-
@user42493 What do you mean by "stalk water equation"? – Ben Grossmann Apr 18 '20 at 19:06
-
Sorry, it was a typo – user 6663629 Apr 18 '20 at 19:08
1 Answers
0
One approach is as follows: with the vectorization operator, we can rewrite the equation as $$ AX + BXC = D \implies [(I \otimes A) + (C^T \otimes B)]\operatorname{vec} = \operatorname{vec}(D) $$
Ben Grossmann
- 225,327