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 May 18 comment Decomposition of a nonsquare affine matrix @tagomago the natorual embedding is given by using homogeneous coordinates as used in the answer. That is a nice trick to transform linear functions in n dimensions to affine functions in n+1 dimensions. Apr 25 comment Decomposition of a nonsquare affine matrix The matrix $A$ needs to be invertible. That means that $det A \neq 0$ and $p \neq 0$. If $p = 0$ we had $a = 0$ and $b=0$ and therefore A not invertible. Jan 22 comment How to define the term closed-form expression? @BillDubuque Thanks for the hint! I searched the archive, but couldn't find any similar question (I marked it as duplicated). The answers and comments there confirmed my suspicion, that it is not always meant to be a really precise term. Anyhow, I'll clarify my question a bit. Dec 22 comment general triangle angles and lengths Yes, both is correct. Nov 14 comment Linear recursion with coefficients depending on n Sorry, you acutally answered my question completly. I had different expectations and didn't want to see that you are right... ;) Nov 12 comment Is there a good proof that all the polynomials in this family are irreducible? Sorry, I improved the answere a little bit. Nov 12 comment Linear recursion with coefficients depending on n You were some seconds faster... :) Since there is a genreal method for all linear recursions, I thought maybe this could be extended to this case somehow. But if you say that you don't think so it's also a very useful answere! Nov 12 comment Linear recursion with coefficients depending on n Yeah you are right of course, but there are helpful methods anyway. Either through generating functions or the characteristic polynomial, see here for example. Nov 12 comment Linear recursion with coefficients depending on n Well also if have specefic $(b_n)_{n≥0}$ and $(c_n)_{n≥0}$, it might be really difficult to find the solution if I dont' have the right idea. I was wondering if there is something like a characteristic polynomial for this case. Oct 7 comment Recursive Generating function for enumerating leaf labeled binary trees Uh yes, thanks a lot! I totally forgot that I've to deal with labeled structures.