# Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
 Views: 302 Announcement: End of year contest, $75+$50 prize! Dec18-13 Meta Thread / Thread Starter Last Post Replies Views Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions... Feb23-13 10:24 AM micromass 1 28,506 Hi, I have to find a vector space V with a real sub space U and a bijective linear map. Here my Ideas and my... Nov30-08 06:30 PM adriank 4 2,306 Is it true that if there is monomorphism from group A to group B and monomorphism from group B to group A than A and B... Jun9-12 05:19 PM DonAntonio 5 1,084 I must apologize if this question sounds dump but if an isomorphism is established between two groups, is it true that... Mar23-13 03:07 PM lavinia 4 645 Apparently there is an isomorphism between the additive group (ℝ,+) of real numbers and the multiplicative group... Jan20-12 02:04 PM SteveL27 3 1,183 The poset on the set of order ideals of a poset p, denoted L(p), is a distributive lattice, and it is pretty clear why... Sep30-10 02:28 AM I<3Gauss 4 1,328 I am having a very hard time with a general concept of proving something. If I have some arbitrary function mapping... Oct2-07 10:53 AM mathwonk 4 1,530 I'm fairly certain the following is a vector space isomorphism \phi :\mathbb{R}^\infty\rightarrow\mathbb{R}^\infty... Jan8-09 07:40 PM jojo12345 4 1,424 Just had an exam there, one of the questions was Partition the list of groups below into isomorphism classes ... May20-11 11:04 AM micromass 3 1,788 Hi, I am wondering if all isomorphisms between hilbert spaces are also isometries, that is, norm preserving. In... Dec28-11 10:38 AM Hawkeye18 17 2,540 if A and B are divisible and there exist monomorphism from A to B and from B to A. Prove that A and B are isomorpic. ... Jun30-12 03:36 AM charlamov 0 474 Can isomorphism of matrix groups \phi: G_1 \rightarrow G_2 always be expressed by \phi(M) = S M S^{-1}? Jul25-08 04:43 AM cathalcummins 16 6,927 The isomorphism of ℝ5 and P4 is obvious for the "standard" inner product space. The following question arise from... Aug18-12 10:58 PM chiro 3 886 We're doing isomorphisms and I was just wondering, is the dihedral group D_{12} isomorphic to the group of even... Jan20-12 03:44 PM Deveno 2 1,144 Hi, I've come across this result which says that if there are two isomorphic vector spaces with a transformation... May21-11 10:02 AM McLaren Rulez 12 1,787 Let V denote the vector space that consists of all sequences {a_n} in F (field) that have only a finite number of... Mar7-05 12:09 AM eckiller 2 1,295 All groups are finite abelian if K⊕K ≅ N⊕N, prove that K≅N I'm thinking of constructing bijection, but I don't... Nov27-11 08:54 PM Bachelier 2 746 Hi everyone. Im new to these forums. I do Computer System Engineering at Brunel university in London. I did Maths and... May2-08 08:47 AM havnek 6 1,245 Does anybody know of a nice, intuitive way to remember the second and third isomorphism theorems? Dec14-07 01:06 AM morphism 2 1,310 wrtie down the possible isomorphism types of abelian groups of orders 74 and 800 then for 74=2*37 then Z(74) is... Nov25-12 07:09 PM cummings12332 2 1,216 Hello. My book offers this statement with no proof, i have been searching in other books with no luck ! I'm... Dec3-07 05:56 PM copper-head 5 3,739 Given: G is the group of matrices of the form: 1 n 0 1 Where n is an element of Z, and G is a group under... Nov26-09 11:54 PM Myriadi 3 1,221 i cant grasp these concepts, 1-to-1 and onto have always annoyed me. here's 1 question, (i dont know how to post... Nov23-04 04:46 AM matt grime 3 1,081 Could someone clearly explain this subject? Going over some linear algebra the moment and I don't see what this topic... Mar27-05 04:24 AM matt grime 1 1,071 Am I doing this right? I'd appreciate any feedback. Let T:U ---> v be an isomorphism. Show that T^-1: V----> U is... May16-05 10:15 PM mathwonk 4 1,582 Hello, let's suppose we are given a set A, a (semi)group S and we define a (semi)group-action t:A \times S... Jun23-10 05:36 PM mnb96 2 753 i was just wondering if someone (matt) could give me a better idea of what the difference is between the two...thanks Aug25-08 03:18 AM tanguyjardin 11 7,890 Ok, here is something i thought i understood, but it turns out i am having difficulties fully grasping/proving it. ... Nov20-08 12:39 AM sutupidmath 4 2,933 Why is Z mod 2 x Z mod 3 isomorphic to Z mod 6 but Z mod 2 x Z mod 2 not isomorphic to Z mod 4? Apr20-09 02:02 AM matt grime 1 892 At the risk of arrousing the ire of the moderaters for posting the same topic in two forums, I again ask this question... Dec7-06 03:52 AM matt grime 20 2,976 It is defined that for any matrix A, A^{0} is defined as being equal to the identity matrix, I My question: Does... Nov21-12 06:32 PM micromass 18 1,611 Not my homework It's in the textbook - lectures of diff geo by s.s.chern Just put them down in a clearer way Could... Jul31-07 09:49 PM mathwonk 5 2,265 I was just wondering why is it so important for certain tools used in physics and engineering to form a group? Like a... Feb17-11 11:21 PM Robert1986 5 854 Alright, this is my case. I am now a former International Baccalaureate Diploma programme student that wrote my... Oct27-05 12:04 PM hypermorphism 14 2,693 So multiplication is an iteration of addition and exponentiation is the iteration of multiplication, i.e. a "second"... Feb12-09 06:20 PM Preno 0 1,022 Iterating Euler's totient function \varphi(n), it eventually arrives at 1. Let h(n) denote the least number of... Jun15-08 04:14 PM huba 1 3,475 Hi. Anyway, learning this sort of makes me feel like I've chosen the wrong school for myself, but I'd like to try and... Mar20-11 06:21 PM ThorX89 5 3,542 I am dealing with a problem,which can be formulated Ax=B,in the first place I wanted to solve it with conjugate... Nov7-11 08:40 AM AlephZero 1 824 Can someone explain if this is true or if there's anything wrong with the following logic? e^ix = cos(x) + isin(x)... Mar10-12 09:31 AM phyzguy 6 1,400 My friend gave me the brain-teaser "i^i = what?", and with a little bit of coaching I finally discovered that i^i =... Sep10-10 03:03 PM Tac-Tics 6 2,160 This is a theorem about Jacobi symbols in my textbook: Let n and m be ODD and positive. Then (a/nm)=(a/n)(a/m) and... Apr17-10 01:10 PM robert Ihnot 1 2,552