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I am looking for the general form of SU(4) matrix.

I believe the answer lies in section 3 or section 4 of the following link : http://arxiv.org/pdf/0802.2634v1.pdf

PS : I don't quite understand Lie Algebra and Group theory in detail and need this for addressing a different problem in my field.

aditya jain
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  • Take a look at this: http://www.ejtp.com/articles/ejtpv10i28p9.pdf – Rocket Man Sep 05 '15 at 14:33
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    Obviously, in order to answer this you will have to know what "SU(4)" means! SU(4) is the set of "special unitary 4 by 4 matrices". Here "special" means it determinant is 1. "Unitary" means that it conjugate transpose (uij is equal to the complex conjugate of uji) is equal to its inverse. – user247327 Sep 05 '15 at 15:04
  • @AJStas Thank you for the link. Can you please explain/ tell me about some resource which explains how to obtain the general parametrization form from the generators? For example : In the case of SU(2) the general form is : ((alpha, beta),(-beta,alpha)) – aditya jain Sep 06 '15 at 09:10
  • @user247327 Thank you for the response. I do understand this much. However I do not understand how to get the general parameterized form given these properties and the generators of the group. – aditya jain Sep 06 '15 at 09:14
  • This might help: http://www.ejtp.com/articles/ejtpv10i28p9.pdf – Shasa Oct 16 '20 at 13:04
  • This link it's already in the first comment.... – user2820579 Mar 17 '21 at 12:48
  • If anyone lands here - this is a good reference to generate random unitaries (typically for studies in quantum computing) : https://chaos.if.uj.edu.pl/~karol/pdf/ZK94.pdf – aditya jain Jul 01 '22 at 04:27

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