  # Dogtanian

Senior Members

30

10 Neutral

• Rank
Quark

## Contact Methods

• Website URL
http://www.oatesfamilyhistory.co.uk

## Profile Information

• College Major/Degree
Maths
1. Oh, I get what you did now. You took the contrapositive of the statement: instead of proving 'if K(v,w)= 0 for a ll w then v=0' you proved 'if v=/=0 then there exists a w such that K(v,w)=/=0'. I think I get it now. So to do this question fro the start you find the matrix K= 004 080 400 in the way it was done above. Then you pick a non-zero v = (a,b,c), say, and fnd a w such that K(v,w)= vKw=/=0. In the case above you found that w=(c,b,a) will work.
2. So, say we to show v =0 for all w.# Let w= a b c-a = (b,a,c) and v= x y z-x = (y,x,z) Then wKv= 8.a.x + 4.c.y + 4.b.z = 0 Now is it simply that for this to be true for all a,b,c then x=y=z=0 automatically?
3. Thanks for telling me K(X,Y) = 4tr(XY). But I thought I'd try to work it out myself anyway as I need it to show how one gets it. I am also able to work out the matrix rep of K you gave. Now, how do I go from here? Do I use this matrix and apply it to a general Y, set this to zero and show that Y must always be zero in this instance? So, I could write a general Y not in the form of a matrix like a b c-a but as a vector a b c as by doing this you clearly see by multiplying the matrix for K with such a vector and setting the answer to zero you must have a=b=c=0.
7. Last I heard (a year or so back) was that the Lib Dems said they would not form any coalition Governemnt with anyone, so if there was a hung Parliament, you can expect another election within a few months (like happend some time in the 70's I believe).
8. Thanks for your suggestions. I will go see my lecturer about it. Only I though't I'd ask here first since it wasn't possible to go see the lecturer before the work had to be handed in (in the morning). Anyway I'd already gone on with the assumption that maximum subgroup meant the largest and it seamed to work out fine for the questions I had. Though I'm still none-the-wiser about maximal v maximum since it turned out I didn't need any results directly relating to maximal subgroups for the questions. I guess I'll find out if I was right in a couple of days...whenever I get the work back or ask the lecturer...which ever is first. Thanks again.
9. Doesn't anyone know? I know semigroups are quite a specialist subject, but I thought someone migth know... ...please
10. I knew there was something about why all this about xnot=x didn't fit...I think you got it there, yes. I'd like to see someone say that you cannot claim that 2 apples are never two apples, no matter which appels you've got. Another example. Say you have 3 chairs : one arem chir, one deckchair and one stool. Youc an say swap the stool for a dinning chair. The stool certainly is different from the dinning chair, but you still have 3 chairs.
11. Can anyone tell me the difference between maximal and maximum subgroups of a semigroup, if there is one at all? I seem to be a bit confused about if there is a difference at all. In my lecture notes I can only find references to maximal subgroups, whereas on a problem sheet I can only find references to maximum subgroups. I also vaguely remeber my lecturer emphasining a difference between maximum and maximal, but I was concentrating on the proof she'd just shown at the time, so I'm not sure if she was talking about a difference within semigroup theory or the difference between semigroup theroy and group theroy. Any clarification would be great
×