What and where is the inverse of a concrete lower triangular matrix?

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Wiwat Wanicharpichat

The above formula of the matrix entries is not correct for j > i. For example, if n=6 then the m_{12}, m_{13}, m_{14} are all "1".

Feng Qi

In my opinion, my expression is correct. For example, $m_{1,2}=\binom{2X1-2-1}{1-1}=\binom{-1}{0}=0$, $m_{1,3}=\binom{2X1-3-1}{1-1}=\binom{-2}{0}=0$, and $m_{1,4}=\binom{2X1-4-1}{1-1}=\binom{-3}{0}=0$. Is it okay?

Just now I found that the answer to this question existed in my previous preprints below. I tried to delete this question, but failed. Sorry for my neglect.

F. Qi, The inverse of a matrix and several identities related to the Catalan numbers and the Chebyshev polynomials of the second kind, ResearchGate Presentation (2017), available online at https://doi.org/10.13140/RG.2.2.22832.46081/1 (Chinese)

F. Qi, Q. Zou, and B.-N. Guo, Some identities and a matrix inverse related to the Chebyshev polynomials of the second kind and the Catalan numbers, Preprints 2017, 2017030209, 25 pages; Available online at https://doi.org/10.20944/preprints201703.0209.v2

I have drafted a general result for the inverse of the above lower triangular integer unit matrix. After a while, I will anounce my concrete conclusion.

This problem has been solved as showed in the picture. I will announce the whole paper soon. Thank you very much for your attention!

Please read the following preprint for the answer to this question:

Feng Qi, Xiao-Long Qin, and Yong-Hong Yao, The generating function of the Catalan numbers and lower triangular integer matrices, Preprints 2017, 2017110120, 12 pages; Available online at https://doi.org/10.20944/preprints201711.0120.v1 or http://www.preprints.org/manuscript/201711.0120/v1

Alimohammad Nazari

Hello Dear

The inverse of unit triangular matrix also is unit triangular matrix and the sign the all entries of lower triangular must be opposite.

With best rgards

Dear Alimohammad Nazari

What do you mean? Have you read my preprint at http://www.preprints.org/manuscript/201711.0120/v1? Is it correct thoroughly?

Dear Feng Qi

please send me full of your paper. I try to answer you after study this paper.

With best regards

Dear Nazari

Please download by yourself the full version from the following address