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Forum: General Questions - Graduate/Advanced
Welcome to the General Questions - Graduate/Advanced forum!
Questions aimed at the post- or advanced undergrad level.

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jump to page: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 >> of 241 (1204 items)

Making matrix invertible by jiku1797 on 2009-11-23 09:41:25
Assume D_1 and D_2 are unitary matrices, P_1 and P_2 are projections with P_1 + P_2 = I (identity). How can I choose matrices A and B so that

(D_1)^* P_1 A P_1 D_1 + (D_2)^* P_2 B P_2 D_2

becomes invertible? (Here the asterisk means Hermitian adjoint.)
[ reply | up ]
Show by a counterexample to that every subgorup of a finitely generated group is finitely generated by carusochu on 2009-11-19 07:54:44
Show by a counterexample to that every subgorup of a finitely generated group is finitely generated.
I cannot find a countereample. Could anyone give me a complete counterexample. Thanks!!!
[ reply | up ]
Significance of finitely presented modules? by EF on 2009-11-15 04:51:37
Hi all,

My graduate course in algebra has recently been covering some results on module theory. However, after defining the concept of a finitely presented module, it has rarely been used as most results we have covered seem to be related to finitely generated modules and modules over noetherian/artinian rings.

I was wondering what major results the property of being finitely presented implies? Are there any canonical type of results relying on this property? What about techniques of proofs that use it?

I know the question is pretty vague, but I'm hoping that someone knowleadgable about the subject could formulate a good question and also answer it. I'm going to ask my professor next, but knowing something helps me to ask him better questions. :)

Thanks.
[ reply | up ]
Let S be a polytope in Rn. Show that S is a closed and bounded set. by angelinelux on 2009-11-14 14:21:28
Let S be a polytope in Rn. Show that S is a closed and bounded set.

How do I show this?
[ reply | up ]
finitely generated group by carusochu on 2009-11-13 16:37:29
How to proof:
 Let G be a finitely generated group(not necessarily abelian),
 and H be a subgroup of G with finite index. Show that H is also
 finitely generated.
[ reply | up ]

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