# 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: 122,579 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 35,106 There are two "formal" definitions of vectors (and tensors in general) which I've learned. The first is what I... Y 06:09 PM micromass 15 174 Hi PF! Can you please tell me why it is beneficial to use SVD in data processing? My understanding is, given a lot... Y 01:54 PM Stephen Tashi 10 237 Hi, 2-forms are defined as du^{j} \wedge du^{k}(v,w) = v^{j}w^{k}-v^{k}w^{j} = \begin{vmatrix} du^{j}(v) &... Y 09:34 AM JonnyMaddox 0 56 Hello. I need some help. I am not a math wizard by any means, but I find myself in need of math right now. I have... Y 07:58 AM Erland 15 484 While studying Yang-Mills theory, I've come across the statement that there exists a positive-definite inner product... Jul29-14 01:21 PM center o bass 0 67 The killing form can be defined as the two-form ##K(X,Y) = \text{Tr} ad(X) \circ ad(Y)## and it has matrix components... Jul29-14 01:19 PM center o bass 0 56 In my limited study of abstract Lie groups, I have come across the adjoint representation ##Ad: G \to... Jul29-14 01:46 AM WWGD 1 318 (I don't like the title, since it is a bit misleading. But, I couldn't think of a more descriptive title that fit in... Jul28-14 01:01 PM Nick O 0 79 Hello, I am trying to understand the slides in the PDF I posted. I am looking particularly at slides 20-24. I am so... Jul27-14 05:57 PM AlephZero 13 551 Hi, all. I'm in desperate need of assistance with a matrix I can't get my head around of. I want to solve a system of... Jul26-14 04:32 PM skujesco2014 1 342 This should be really easy, but I can't seem to find the answer. What does the symbol ##\ominus## mean in the context... Jul26-14 06:45 AM HallsofIvy 2 344 Hi, I have a rather trivial question but google did not really help me. So far I was always familiar with the fact... Jul24-14 11:23 PM divB 5 572 I heard about fast tridiagonal matrix algorithm. I tried to find what is it but I can only find tridiagonal matrix... Jul23-14 11:58 AM Shyan 0 451 Just one simple doubt here. Can we use different scales on the x and y axes be used for denoting linear... Jul22-14 06:48 AM HallsofIvy 2 811 I know it should be absolute zero, but in a scientific calculator, which is an app actually, its value is shown... Jul21-14 05:34 AM Adit 3 481 Hello, I am going over these slides and I am very confused on a couple parts. First of all on the first slide, I... Jul20-14 01:19 PM WWGD 6 572 Hello everyone! I've been learning some basic group theory (I'm new to the subject). And I had a (hopefully) fairly... Jul19-14 06:37 PM WWGD 3 559 Hi,let: 0->A-> B -> 0 ; A,B Z-modules, be a short exact sequence. It follows A is isomorphic with B. . We... Jul19-14 03:16 PM WWGD 4 1,433 Problem 1: Use Gaussian elimination with back substitution to solve the following system. Problem 2: Use the... Jul19-14 12:38 PM micromass 6 930 Hi, Given several vectors, which may be or not be orthogonal to each other, how to construct a vector perpendicular... Jul18-14 06:25 PM WWGD 4 728 I am working with polytopes that are defined by half-planes in \Re^N. So they are defined by a number of inequalities... Jul18-14 04:11 PM sloppyintuit 2 687 Hi All, Let A,B be algebraic structures and let h A-->B be a bijective homomorphism. Is h an isomorphism? In... Jul18-14 12:01 PM WWGD 2 873 Use Gaussian elimination with back substitution to solve the following system: x1+x2+x3=1, x1+2x2+2x3=1,... Jul17-14 09:34 PM Math10 3 1,039 Hello, Been a long time lurker, but first time poster. I hope I can be very thorough and descriptive. So, I have... Jul16-14 04:02 AM nikphd 4 1,425 Hi all, Suppose I have a matrix A_{N\times N}. I compute its eigenmodes A V = V \Lambda. V, \Lambda are... Jul15-14 08:06 PM AlephZero 1 1,162 The killing form on a lie algebra is defined as $$B(X,Y) = \text{Tr}ad_X \circ ad_Y$$ where ##ad_X: \mathfrak{g} \to... Jul14-14 05:44 PM Terandol 1 1,451 Hello, Given the complex linear mapping: T(z) = Az + B where A is real and B is complex. However trying to show... Jul14-14 03:57 PM WWGD 3 1,169 The definition (taken from Robert Gilmore's: Lie groups, Lie algebras, and some of their applications): We have... Jul14-14 01:22 PM Travis091 6 1,345 Two groups are isomorphic if they has same number of elements and if they has same number of elements of same order?... Jul5-14 05:24 PM NeoAkaTheOne 12 5,602 Can you guys give me a concrete example of a completely positive map from M_m → M_n? Jul3-14 06:26 PM WWGD 2 2,426 Hi, i was wondering how the following expression can be decomposed: Let A=B°C, where B, C are rectangular random... Jul2-14 04:54 PM MisterX 2 2,495 I am trying to diagonalize the following matrix: M = \left( \begin{array}{cccc} 0 & 0 & 0 & a \\ 0 & 0 & -a &... Jul2-14 12:45 PM Trifis 2 1,958 I need help solving for t in the following equation, |P + Vt + A(t^2)/2| = st where P V and A are vectors and s... Jun30-14 04:45 PM jedishrfu 3 2,221 I've been reading about algebraic geometry lately. I see that a lot of authors use ##V^\vee## to denote the dual space... Jun29-14 10:45 AM Mandelbroth 2 2,671 Hi. In this development (c ∇+ d A)(c ∇+dA)= c^{2} ∇^{2} + d^{2}A^{2} + cd A∇ + cd ∇A (c ∇+ d A)^{2}= c^{2} ∇^{2}... Jun28-14 11:49 AM Fredrik 9 2,103 Hi, Can someone explain me the division operation in the picture. First for left division we use (.\ ) not only ( \ )... Jun26-14 06:22 PM HallsofIvy 4 2,051 I was reading in my textbook that the scalar product of two complex vectors is also complex (I assuming this is true... Jun23-14 08:16 AM Fredrik 4 1,960 Hello, first of all, sorry if my question is either trivial or imprecise, I'm from the engineering domain :) I... Jun23-14 06:26 AM Erland 1 1,922 Hey, So I am trying to do a tri-quadratic curve fit (linear regression) in excel. I have successfully completed a... Jun20-14 11:37 AM mattskie 2 1,990 1. Is there a general condition for the existence and uniqueness of solution of a system of simultaneous non-linear... Jun19-14 07:40 AM Chestermiller 7 2,178