Recent content by etnad179

Hi All, I recently came across the interesting notion of constructing the minimal set of nxn matrices that can be used as a basis to generate all nxn matrices given that matrix multiplication, and addition and multiplication by scalar are allowed. Is there a way to construct an explicit set...

Hi, thanks for the help - I've been looking at this for a bit and I think I understand most of it. Just to check the \tau is the set of permutation of the elements {i_1,...i_n}? And how can we get from this permutation \tau of the row is equal to the inverse \tau^{-1} of the column for...

Oh well, thanks for the help! Really appreciate it!

Hmmm - that makes some sense. So my definition of a discrete group (being one that is totally disconnect) is incomplete? Also, would you know how this idea of open sets links with what physicists call discrete groups? i.e. groups with discrete elements? Thanks so much!

I took the definition of discrete group to be one that is totally disconnected... I would have thought that if the set of singletons was open, one could always go to another group element by following some connected path? If the singletons were closed, I would have guessed that then you...

Sorry, I'm quite new to this - I might just be missing a definition... but why is the topological group discrete if the set is open?

Hi thanks for your quick reply. I'm still a little confused - the singletons of G/H are open is fine - but why does that imply the topology on G/H is discrete?

Excellent! Thanks - I thought there may have been an easy and well documented way to do it!

I used to know how to prove the statement for matrices det(AB)=det(A)det(B) concisely but for the life of me I've forgotten it... Does anyone know a concise proof for this? Thanks!

Hi All, I've come across a theorem that I'm trying to prove, which states that: The quotient group G/H is a discrete group iff the normal subgroup H is open. In fact I'm only really interested in the direction H open implies G/H discrete.. To a lesser extent I'm also interested in the H...