# 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: 125 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 35,753 I am somewhat confused with the connection between the two groups. In the text I'm reading (An Introduction to... Y 10:39 PM Ben Niehoff 4 148 Z = field of integers . If R is a ring and k is an element of Z, write kR = {kr | r is an element of R}. It is... Aug19-14 03:23 PM Erland 3 138 Hi everybody, do you have an efficient method for build up a vector with random components which is perpendicular... Aug19-14 10:07 AM Chandrasekhar 6 161 Can anyone explain the idea behind Hadlock's proof that there is an Sn for every poly of degree n? Theorem 37 page... Aug19-14 09:59 AM Ray 3 291 Hello again PF! I had a question on singular value decomposition. My question relates to a pepper I have been... Aug18-14 11:51 PM AlephZero 10 351 Hi all, Just doing a bit of personal study on vector spaces and wanted to clear up my understanding on the... Aug18-14 06:42 AM "Don't panic!" 2 161 This lemma the book states, I can't make sense of it. Lemma: If a,b\in Z and b > 0, there exist q,r \in Z such that... Aug16-14 02:11 PM lants 3 138 How can we deform a given Lie algebra? In particular, in the attachment file how can we arrive at the commutation... Aug16-14 05:39 AM Esmaeil 0 134 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... Aug15-14 10:23 AM Pond Dragon 2 342 I've found this paper: Closed Expressions for Lie Algebra Invariants and Finite Transformations and I've attempted to... Aug14-14 11:20 PM Greg Bernhardt 1 321 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) &... Aug14-14 11:20 PM Greg Bernhardt 1 325 Dear Friends, Please tell me the differences created in ring theory problems when 1.Unity is taken in integral... Aug14-14 08:27 PM jbunniii 3 176 I have a non symmetric matrix AB where A and B are symmetric matrices. How can I find the eigenvectors and eigenvalues... Aug14-14 06:17 PM dmytro 1 157 In the US, food products have an ingredient list and a "Nutrition Facts" panel. The ingredient list lists all... Aug14-14 11:36 AM Stephen Tashi 3 169 Why do we need fields (Why do we define fields?)for linear algebra? Aug14-14 12:45 AM homeomorphic 10 227 hey pf! can you help me understand what an adjoint operator is? i've read lots of threads and other sites, but am... Aug13-14 10:50 PM Fredrik 10 309 (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... Aug13-14 01:55 PM Nick O 2 325 Let e_i be a unit vector with one 1 in the i-th element. Is the following expression has a recursive presentation? ... Aug13-14 10:43 AM regina_lee 2 216 I heard about fast tridiagonal matrix algorithm. I tried to find what is it but I can only find tridiagonal matrix... Aug12-14 05:21 AM Shyan 2 760 Hi all, I have been searching around and cannot seem to find an answer. I am doing a past paper, and have the answers... Aug11-14 03:21 PM mathman 1 296 Quick version: I have a vector field f:\mathbb{R}^n\oplus\mathbb{R}^m \to \mathbb{R}^n of two arguments x \in... Aug11-14 07:11 AM dmytro 3 368 Could anyone help me solve this problem? Let A,B be two subspace of V, a \in A, b \in B. Show that the following... Aug7-14 06:51 AM schw 2 279 Hi, Just wondering when using the Euclidean Algorithm to find gcd of 4+7i and 1+3i. Where does 2 and 2+i come from... Aug7-14 12:11 AM mathwonk 6 306 Hi, I have an ordinary least squares setup y = Ac where A is an NxM (N>>M) matrix, c the unknown coefficients and y... Aug4-14 07:00 PM mfb 7 380 There are two "formal" definitions of vectors (and tensors in general) which I've learned. The first is what I... Aug3-14 06:09 AM Fredrik 17 595 While studying Yang-Mills theory, I've come across the statement that there exists a positive-definite inner product... Aug2-14 11:49 PM Terandol 3 386 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... Aug2-14 10:34 AM WWGD 7 1,885 Hello, my problem is the following: A lasers gives out a bunch of data points which are reflected off a metal... Aug1-14 01:48 PM chogg 2 313 Hi PF! Can you please tell me why it is beneficial to use SVD in data processing? My understanding is, given a lot... Jul30-14 01:54 PM Stephen Tashi 10 544 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... Jul30-14 07:58 AM Erland 15 777 In my limited study of abstract Lie groups, I have come across the adjoint representation ##Ad: G \to... Jul29-14 01:46 AM WWGD 1 558 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 13 847 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 1 585 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 2 577 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 5 932 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 1,109 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 3 763 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 6 850 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 3 848 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 1,780