I need a reference to the integral analogue of Cauchy-Binet identity, but I can not find such a reference. Could you please help me? Thank you in advance.
Dear @Feng, in addition to the article given by dear @Praveen, I suggest the following article entitled:"Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities II. Grassmann and quantum oscillator algebra representation" by Sergio Caracciolo and Andrea Sportiello at the link:
http://arxiv.org/abs/1309.7916
I hope that this helps,
Abedallah Rababah
Dear Feng Qi, this may help:
Lemma 3.1 in
https://deepblue.lib.umich.edu/bitstream/handle/2027.42/70445/JMAPAQ-44-8-3657-1.pdf?sequence=2
or
https://books.google.sk/books?id=218uQwAACAAJ&dq=inauthor:%22Constantin+A.+H.+Andreev%22&hl=sk&sa=X&ved=0ahUKEwjGh4f1m9fMAhVhBMAKHWzjD1oQ6AEIGzAA
Best regards, Viera
Dear Viera,
I can not access to the second website, could you please write down here the full information about the book by Constantin and Andreev: Authors, Book Title, Press Name, Publishing Year, and the like?
Your information is very very important for me, thank you very much.
Feng
Dear Feng Qi, I am sorry,
I will send you an e-mail.
Best regards, Viera
Dear all
What are the dfferences between the following references? The same one?
[1] C. Andr\'eief, Note sur une relation les int\'egrales d\'efinies des produits des fonctions, M\'em. Soc. Sci. Bordeaux 2 (1883), 1--14.
[2] C. A. H. Andreev, Note sur une relation entre les int\'egrales d\'efinies des produits des fonctions, par M. C. Andr\'eief, impr. de G. Gounouilhou, 1884; Available online at https://books.google.sk/books?id=218uQwAACAAJ.
Feng
Dear Feng,
I think the contribution of Andréief is the same in both.
In 1883, it was published as a paper or short notice by the author.
A year later, it was published together with other works in a book or a greater journal. This one has another "author (M.C.Andréiev - in fact, he was editor)", apparently a relative (maybe a son, what I deduce from C. as the second letter of his name
Dear Viera
Thank you for your so detailed explanation. However, I am not understand something yet.
(1) Who's who? Do you mean C. Andr\'eief is perhaps the father of M. C. Andr\'eief? M. C. Andr\'eief=M. C. Andréiev? Who is C. A. H. Andreev? Konstantin Alekseevich Andreev=Constantin Alekseevich Andreev? C. A. H. Andreev=Constantin Alekseevich Andreev? This is a headache for me.
(2) Do you mean that I should cite the following reference and ignore the reference [2] mentioned above?
[1] C. Andr\'eief, Note sur une relation les int\'egrales d\'efinies des produits des fonctions, M\'em. Soc. Sci. Bordeaux 2 (1883), 1--14.
By the way, Lemma 3.1 in [3] below was recommended by you, it was cited from [1], and, as I said before, it is useful for me to compose a manuscript. Thank you.
[3] J. Baik, P. Deift, and E. Strahov, Products and ratios of characteristic polynomials of random Hermitian matrices, J. Math. Phys. 44 (2003), no. 8, 3657--3670; Available online at http://dx.doi.org/10.1063/1.1587875.
Best regards
Feng
Dear Feng,
my answers to your questions are:
(1) yes, C. or C.A. or C.H.A. is still the same Andréef.
Апдреев is the exact russian form. Written transcription is Andreev, pronunciation is Andréief.
My name is Čerňanová, by foreigners often written as Cernanova.
It´s a similar situation with Konstantin - Constantin, Andreef - Andréief - Andreev ...
(2) yes
The first time I posted both, since I didn´t know which one could be obtained from internet more easy.
Finally I vote for 1883, because it was the first time that the result was published.
Really, the same is cited in Lemma 3.1 in [3] that I recomended before.
Viera
Dear Viera
Thank you very much for your detailed answers to my questions. Now I have increased some knowledge about pronounciation in Russian and the like. I will cite the reference by [1] above.
Moreover, if I could use the Cauchy-Binet (Binet-Cauchy) formula to complete a previous draft on the logarithmic concavity for the Riemann Zeta function, I would acknowledge you and others, who ever gave me a hand, in the final work.
Best regards
Feng
Dear Feng, [1] is the best choice.
Just a remark: in the work [3] that we mention above, a word dropped out. The right citation is
[1] C. Andréief: Note sur une relation entre les intégrales définies des produits des fonctions, Mém. Soc. Sci. Bordeaux 2 (1883), 1--14.
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