# 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 Views: 123,384 Announcement: Follow us on social media and spread the word about PF! Jan16-12 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 35,138 Hi guys, Let's say I have a 6x6 matrix A whose Jordan form J has 3 Jordan blocks. It means that this matrix (matrix... Dec3-12 10:24 PM fluidistic 18 3,104 How are orbits and cosets related? Are all orbits cosets? Are all cosets orbits? Also, what exactly are G-sets and... Nov30-12 10:09 AM lavinia 1 1,130 Hello, I want to find a family of functions \phi:\mathbb{R} \rightarrow \mathbb{C} that have the property:... Nov28-12 03:30 PM lavinia 14 1,759 I thought it would be obvious, but I can't find a series representation of the Laplace transform. I'm looking for... Nov29-12 08:48 AM lurflurf 2 995 I have two 3d applications and when an object(a cube for example) is transferred between them, the rotation values of... Nov28-12 08:06 AM HallsofIvy 3 801 It's very difficult for me to find any simple literature to explain this idea. J\inMn(ℂ) is a coninvolutory (or a... Nov29-12 01:42 PM rasmhop 4 914 Hello, let's suppose I have two functions f,g\in L^2(\mathbb{R}) and I consider the inner product \left\langle f,g... Nov29-12 06:54 PM Stephen Tashi 7 1,398 Given two systems, Ax=b and Cy=d, for nxn matrices A and C, and n-dimensional vectors b and d, each of which has at... Dec1-12 12:21 PM Erland 1 889 The following problem was given on a test of mine and I got it completely wrong. If anyone can help me with solving... Nov29-12 06:09 PM jgens 1 765 After solving some problems about matrix invertibility and learning some theorems (and proving them), I have developed... Dec1-12 01:22 PM Bipolarity 2 817 Hi guys I wonder if you know any linear algebra formalism or something to solve the following question... Dec3-12 10:37 AM phynewb 3 996 I now know that inverses are only defined for square matrices. My question is: is this because inverses for non-square... Dec2-12 06:57 AM HallsofIvy 8 1,092 let A_i be an odd integer, s_i be the square of a_i and t_i be the triangular number, (s_i -1)/8. Same for a_j , s_j,... Dec1-12 10:25 PM Norwegian 2 1,375 At first I thought that there is no square matrix whose square is the 0 matrix. But I found a counterexample to this.... Dec2-12 12:37 PM Bipolarity 5 1,080 Bocard's problem asks to find the solutions to the Diophantine equation n!=m^2-1. The only known (n,m) pairs are... Dec9-12 05:46 PM Someone2841 3 1,754 I am trying to find a way to generate solutions to 5b^2*c^2 = 4a^2(b^2+c^2) Can anyone offer some insight? I... Dec13-12 06:26 AM ramsey2879 55 7,188 the question is , if f(n)= 1+10+10^2 +... + 10^n , where n is integer. find the least n s.t. f(n) is divisible by 17... Dec5-12 09:33 AM Edgardo 3 1,301 Hi, If A is some nonsquare matrix that is possible rank-deficient, then am I right to understand that (A^T)(A) is a... Dec5-12 09:16 AM D H 1 1,791 Hi. There is a polynomial f = (x^3) + 2(x^2) + 1, f belongs to Q. It will be shown that the polynomial is irreducible... Dec5-12 06:36 PM Square1 1 744 I am curious about the proof of the fact that the value of a determinant computed using the Laplace (or cofactor)... Dec6-12 12:09 PM micromass 1 692 I need some help understanding the following definition: Definition: Let A\inMn(ℂ) the complex vector space ... Dec8-12 09:11 PM BrainHurts 4 823 Hi Can anyone help with understand a basic idea, I have a matrix A in MATLAB which is 100x3000. I have checked... Dec6-12 08:04 AM mikeph 2 708 If I have a matrix valued function A(x) of some scalar x, how do I compute the derivative of the square root of A with... Dec9-12 09:35 PM bpet 4 1,834 3.5036799918564934004113 I need help identifying this real number. The closest I have gotten is e+pi/4. But I... Dec9-12 11:53 PM haruspex 9 1,925 I recall a post previously where the Op was wondering if any circle about the orgin having an irrational radius could... Dec8-12 09:43 PM ramsey2879 4 1,356 I'm not a mathematician of any sort so excuse me if my question is stupid. I just realized that I could not define... Dec10-12 10:52 PM jedishrfu 3 1,429 on page 261 of this paper by J. Vermeer (http://www.math.technion.ac.il/iic/e..._pp258-283.pdf) he writes The... Dec9-12 09:38 PM BrainHurts 4 819 Is anyone interested in learning some algebra? I was planning to go through Dummit and Foote (I have some basic group... Dec9-12 01:56 AM sammycaps 0 660 The proof goes as follows: For contradiction, assume there exists |s|< ∞ such that s = {e1, e2, ... , en} and... Dec11-12 07:51 AM mfb 1 561 Ok I promise this time it is not a homework type question. If someone could direct with a name of a theorem here,... Dec12-12 08:54 PM Square1 3 762 I've been reading a few mathematical definitions and I'm still not sure I grasp their significance. If Ax = b, then... Dec13-12 04:42 AM mikeph 9 1,413 I'm still confused about L U matrix factorization. I'm trying to understand how to do it and why doing so is... Dec11-12 03:00 PM symbolipoint 4 1,027 Hi All, I've been following a group theory course which I am struggling with at the moment. I'm from 3 different... Dec11-12 07:36 AM AlbertEi 4 863 Hey! I am studying group theory for particle physicists right now and I came across the following general question... Dec11-12 01:24 AM CuriosusNN 0 639 So this is a pretty dumb question, but I'm just trying to understand homomorphisms of infinite cyclic groups. I... Dec14-12 09:34 AM sammycaps 10 1,239 I am not sure which rubric this belongs to, but since the zeta function is involved, I am putting it here. I noticed... Dec12-12 11:15 PM nomadreid 0 1,122 Can someone please explain to me, in as simple words as possible, what a quotient group is???? I hate my books... Dec13-12 08:05 PM algebrat 2 744 A 3x3 symmetric matrix has a null space of dimension one containing the vector (1,1,1). Find the bases and dimensions... Dec14-12 01:21 AM MoBaT 3 621 Hi guys, I am not a physicist but saw that you guys are actively discussing math problems in this forum. I have the... Dec14-12 04:34 PM chiro 1 709 Suppose we have a dynamical system x_{t+1} = Ax_{t} where A is matrix, x is vector. We suppose that $x$ always grow as... Dec15-12 08:29 AM pasmith 1 683