# 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: 86,424 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 34,210 I imagine a matrix group, with multiplication as the composition rule, to always possess the quality of having centre... Feb20-14 01:57 PM pasmith 3 466 Am i correct if I say that Fiedler number surges when percolation is at percolation threshold? Assume a randomly... Mar8-13 10:44 AM kosmos 0 467 Dear All: For a line structure(say a very long atomic chain) and a closed loop structure( connect the head and tail... Oct31-13 10:59 PM peter308 0 467 How I do for calculate the solid angle formed by 3 vectors like: http://s30.postimg.org/61lpvmi4h/solid.jpg ? Feb18-14 11:15 AM Jhenrique 2 468 Given the following: $$\\ \begin{bmatrix} A & 0\\ 0 & B\\ \end{bmatrix}$$ the eigenvalues is exactaly A and B. So... May20-14 08:43 PM Matterwave 5 469 If the group G/ is abelian then how do we show that xyx^{-1}y^{-1}=1? Thanx May26-14 03:09 AM homeomorphic 3 469 Hi there. I would like to learn more, if any, on interesting applications of Euclidean rings both in mathematics,... Jun23-13 04:33 PM jamesb1 0 471 okay so i'm having some conceptual difficulty given some vector space V (assume finite dimension if needed) ... Apr9-14 08:07 AM HallsofIvy 6 471 I am trying to understand Galois Theory and reading through various theorems and lemmas, some of which are still... May14-14 10:52 PM Boorglar 2 472 Let L: R3 -> R3 be L(x)= \begin{pmatrix} x1+x2\\ x1-x2\\ 3x1+2x2 \end{pmatrix} May20-14 03:11 AM sudhirking 6 472 Hi everyone, I have a square matrix J \in \mathbb{C}^{2n \times 2n}... Feb27-14 11:57 AM Sam1984 0 473 Is it? Personally, I think it is since the max power on any unknown is 1, no trig function, no product of unknowns... Oct12-12 02:20 PM Studiot 1 475 If I have (α1,β1,γ1) and (α2,β2,γ2) as two set of rotation angles in radians.Where α is Yaw of α about z axis, β is... May15-14 07:09 PM abubakr 4 475 If I have two square nonnegative primitive matrices where the Perron-Frobenius Theorem applies how would I calculate... Jul4-13 09:01 PM Simon Bridge 2 476 There are lots of examples of numbers where "is it a rational number" has been an open question for a while before... Jun21-13 01:54 PM Office_Shredder 0 477 I have been trying to implement this Wave equation into java: A = amplitude of wave L = wave length w... Feb3-14 06:09 AM pasmith 1 477 Is there an expression, in general, for the product of two matrix exponentials, for non-commuting matrices? i.e.... Apr1-14 12:36 PM micromass 1 477 Hi, all: Say we have a bare-bones Vector Space v, i.e., V has only the basic vector space layout; no... Apr27-11 04:47 PM micromass 1 478 I'd like to figure out why f(x) = x^n - r e^{i \theta} = \prod_{j = 0}^{n - 1} ( x - r^{1/n} e^{i \theta / n} e^{2... Feb9-14 03:33 PM AlephZero 2 478 Here it is for those interested. http://arxiv.org/pdf/1305.2897.pdf May28-13 08:47 AM epsi00 0 479 Hi, All: I have seen Orthogonal groups defined in relation to a pair (V,q) , where V is a vector space , and q... Jun10-11 09:11 PM Bacle 0 480 So in our notes we are given a general quadratic equation in three dimensions of the form: Ax^2 + By^2 + Cz^2 + Dxy... May6-14 08:04 PM cooev769 2 480 I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and... Oct30-13 11:54 PM Math Amateur 2 480 Hi, I have found an encryption algorithm named ECKS-PS (published in a paper named 'efficient conjunctive keyword... Apr10-13 03:13 AM sanderpotter 0 481 The two properties every linear transformation T: V -> W has to satisfy is T(u + v) = T(u) + T(v), for u,v in V (i)... Feb17-14 04:01 PM jgens 4 481 is it true that \frac{1}{g_{ab}}=g^{ba}? I am a bit confused by the index notation. I especially wonder about the... Apr6-14 06:12 PM HallsofIvy 3 481 The linear combinations of V = (1,1,0) and W = (0,1,1) fill a plane. My question is how do i describe that plane?... May25-14 08:28 PM HallsofIvy 3 481 The Fourier series can be used to represent an arbitrary function within the interval from - π to + π even though... Jun28-13 03:39 PM tiny-tim 1 483 I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and... Oct30-13 10:52 PM Math Amateur 2 484 ... I think I've misunderstood their definition of an invariant. The pth power of the trace function seems to... Nov25-11 04:06 AM Rasalhague 0 485 Hello, I was "playing around" with the S_{3} Young Tableaux, and trying to calculate the Young Operators for them...... Dec13-13 01:33 PM ChrisVer 0 487 Do you know any example of matrix which is not symmetric and has real eigenvalues? Apr24-14 03:20 AM maajdl 1 487 Is it possible for a variable to exit the basis and after a couple of iterations, enter it again? Are there any... Jun9-11 09:31 AM arthurav 0 488 Is it correct to state that a diagonalizable endomorphism has always kernel = {0}? Dec14-13 01:14 PM Daaavde 6 488 Hi, let G be any group . Is there a way of embedding G in some other group H so that G is normal in H, _other_ than... Apr25-14 06:10 PM micromass 1 488 Problem 1: Use Gaussian elimination with back substitution to solve the following system. Problem 2: Use the... Jul19-14 12:38 PM micromass 6 490 Can someone tell me why Sum from j=1 to 3 of y_j*(x'_j , x'_k) = (f , x_k) for 1<=k<=3 where (x1,x2) is the... Mar28-13 06:18 PM ericm1234 0 491 Dear All: For a line structure(say a very long atomic chain) and a closed loop structure( connect the head and tail... Nov1-13 08:30 AM HallsofIvy 4 491 I'm trying to understand in an applied sense what could a change of basis based on a transformation matrix consisting... Dec7-13 09:06 AM TheOldHag 0 491 given the scalar product (Uf | Uf) = (e^{t}f |e^{t} f) with U=exp(tA) for an operator A , what condition... Apr17-11 04:52 AM zetafunction 0 492