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Feb 18, 2011 at 11:25 comment added Gerry Myerson @alex, absolutely right, I should have written $A^{k+1}B^TDBA^{k+1}-B^TDB$. @Peter, this site caters for mathematicians doing research. I expect any research mathematician to be able to work out how $AXA$ relates to $X$ when $A$ is diagonal and go from there. If you can't, you've come to the wrong site. Have a look at the faq, and the alternative websites mentioned therein.
Feb 18, 2011 at 9:11 comment added Peter Is it easy to solve $AXA-X=C$ ? Could you give materials related to this formula?
Feb 18, 2011 at 6:42 comment added alex I think you forgot to account for the $i=0$ term. To see this, note that the equation you write down has no solution when $A$ is the identity matrix.
Feb 18, 2011 at 6:22 history answered Gerry Myerson CC BY-SA 2.5