# Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
 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 09:24 AM micromass 1 30,541 For the transposition (i j)(k), this is what I have in my notes: (i j)(k) = k if k is not equal to i or j (i j)(k)... Jan30-13 08:55 AM Artusartos 2 560 Page 5 in this link: http://doctorh.umwblogs.org/files/2010/10/honors_brown.pdf I couldn't really understand... Jan30-13 08:47 AM Artusartos 4 768 hi , this result is from text , Abstract Algebra by Dummit and foote . page 120 the result says , if G is a... Jan29-13 01:16 PM Maths Lover 6 790 Hello, it is known that "Every regular G-action is isomorphic to the action of G on G given by left... Jan28-13 04:09 PM mnb96 2 743 I am currently looking at a number sequence to solve a puzzle. I have identified the following with the sequence: ... Jan28-13 04:12 AM dodo 2 995 Let y=Ax. A is a matrix n by m and m>n. Also, x gets its values from a finite alphabet. How can i show if the mapping... Jan27-13 04:47 PM acco40 3 719 If you consider a bounded linear operator between two Hausdorff topological vector spaces, isn't the kernel *always*... Jan27-13 11:15 AM micromass 1 905 My book goes on to say: "If we consider both C^n and C^m with norms, then we define the norm of an M x N matrix A... Jan27-13 08:23 AM Fredrik 4 875 hi, I understand how to do the rotation equation A = A*v = y ] xsinθ + ycosθ ] A*v = ... Jan27-13 05:33 AM Simon Bridge 1 594 Let's say I have a vector (4+2i, 1-i), how do I take an L2 norm? Dont tell me I simply do sqrt(16+4+1+1)..? Jan27-13 12:21 AM jbunniii 1 900 Greetings. I am new to the forums. I will try and keep this short. Linear Independence vs Linear Dependence.... Jan26-13 02:03 PM Gipson 38 2,668 Hi. I'm trying to determine the CFL condition for the fourth-order leapfrog scheme. I'm finding 2 as what's... Jan26-13 01:15 PM wrechtin 4 1,414 When the book says "Members of ] are linear combinations of linear combinations of members of S". basically means the... Jan26-13 10:56 AM Fredrik 3 777 Hi, I'm learning about vector spaces and I would like to ask some questions about it. Suppose I have a vector space... Jan25-13 04:57 PM lavinia 5 929 Hello, :) I would like to minimize and find the zeros of the function F(S,P)=trace(S-SP’(A+ PSP’)^-1PS) in respect... Jan25-13 06:04 AM GoodSpirit 3 802 hey guys so i am well familiar with finding out rank of square matrices but if matrix is just a row or column vector... Jan24-13 01:21 PM shivaniits 9 963 a = xyz b = xy+xz+yz c = x + y + z How do you solve x, y, and z? Jan23-13 04:46 PM mfb 3 876 In the book it states that the span of the empty set is the trivial set because a linear combination of no vectors is... Jan23-13 07:24 AM HallsofIvy 3 964 The question is which sets of natural numbers are closed under addition. I know that odd is not, and I know how to... Jan23-13 03:23 AM lurflurf 2 837 Hi all. I have a question about the properties of the generators of the SO(N) group. What kind of commutation... Jan22-13 01:44 AM Einj 3 873 From my textbook: A free R-module is "A left R-module F is called a free left R-module if F is isomorphic to a... Jan21-13 02:51 AM algebrat 1 984 Hi all, I searched all other threads but was unable to find something useful. Here is my question: I am looking... Jan20-13 03:06 PM Wrukproek 0 618 Prove the Generalized Associative Law for Groups (i.e. a finite sum of elements can be bracketed in any way). The... Jan20-13 12:55 PM Fredrik 6 1,354 A Theorem in our textbook says... If R is a PID, then every finitely generated torision R-module M is a direct sum... Jan18-13 03:00 PM mathwonk 1 897 Dear Friends & Colleagues, I have a couple of nagging issues with mathematics I was hoping any one of you would... Jan18-13 10:42 AM Stephen Tashi 5 2,182 Following is a list of 39 Mersenne numbers. Some are prime and some are not. These are generated with x =(... Jan17-13 08:06 AM arydberg 6 1,228 hey guys given Ax=B where A is a square matrix and x and B are vectors, can anyone tell me why a singular matrix... Jan16-13 08:38 PM joshmccraney 3 982 I was thinking about the following proposition that I think should be true, but I can't pove: Suppose that F is a... Jan16-13 05:59 AM lavinia 2 922 Hi, For any odd composite 'N', let u = (N-1)/2, v = u+1, then u^2(mod p) = v^2(mod p) if and only if 'p' is a... Jan16-13 02:49 AM dodo 1 889 My textbook says that... If M is a left R-module, then a submodule N of M...is an additive subgoup N of M closed... Jan15-13 09:33 PM mathwonk 3 730 I'm unable to understand this generalization of vectors from a quality having a magnitude and direction, to the more... Jan14-13 10:29 AM danzibr 4 1,278 In this video: http://www.youtube.com/watch?v=FZz-Q-KBlpE At the time 2:10, I don't understand why we have to... Jan14-13 07:15 AM Artusartos 4 1,009 Perhaps forum members can advance science by solving this optimization problem from The Protein Engineer ... Jan13-13 04:10 PM homeomorphic 2 785 I don't know if this is the correct section to post this, but does Galois theory has any applications in physics? Jan13-13 03:47 AM Jim Kata 2 1,770 Pretty much what the title says. Suppose we have a topological vector space $(X,\tau)$ and $U\subseteq X$ is... Jan12-13 09:32 AM danzibr 5 1,137 Hi all, I have been asked the question by a friend of mine who was working on a computer algorithm where he needed... Jan11-13 03:01 PM HallsofIvy 4 1,171 Hello all, I am new to this forum but am glad I found it, I have a quick question about condition numbers and order... Jan10-13 06:08 PM AlephZero 5 1,089 Hello, I was wondering if this problem is one that is solvable, and if so, if I would be able to solve it in a... Jan9-13 11:31 PM hello95 3 1,013 Hey guys, lurked here a bit, but now I'm in this new math course right. So anyway it seems like a completely new... Jan9-13 06:59 PM sniper_spike 4 799 Hi guys, first post! I'm doing some side work on coupled oscillating systems, and I've almost found a procedure to... Jan9-13 03:39 PM Jack Jenkins 0 826