# 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: 2,524 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 35,955 Hi, I just want to see if I understood this. Since the geometric product is associative and so on we can write for two... Y 05:16 PM JonnyMaddox 0 85 Dear all, Please read the text in the attachment. Then...... 1)Explain what is meant by "fix k" and "fixed point... Y 11:50 AM Stephen Tashi 13 1,888 Hi, I'm having a bit of difficulty with the following definition of a linear mapping between two vector spaces: ... Aug31-14 04:55 PM FactChecker 7 377 - - - Hey everyone, I've got a question in elementary group theory. Suppose we have a group G, and we want to completely... Aug31-14 07:22 AM micromass 5 202 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... Aug30-14 06:08 PM WWGD 4 315 Hi all, I was asked by someone today to explain the notion of linear independence of a set of vectors and I would... Aug30-14 05:12 PM WWGD 15 257 How can we deform a given Lie algebra? In particular, in the attachment file how can we arrive at the commutation... Aug28-14 04:49 PM Greg Bernhardt 1 277 hello every body. may i know what is the difference between geometric product and tensor product ? Aug27-14 07:48 PM mikeeey 2 200 Is -(x^-1) = (-x)^-1 true for all nonzero x in any ring, where x^-1 denotes the multiplicative inverse of x? Aug26-14 02:25 PM 1MileCrash 20 550 I've seen it often taught that the combination of two vectors is their graphical sum, but I think that there is a... Aug23-14 07:18 PM mfb 4 366 I am trying to self study linear algebra. This might seem like a very silly question but what does R subscript 3 mean... Aug22-14 10:58 AM HallsofIvy 4 303 Hi, I have an ordinary least squares setup y = Ac where A is an NxM (N>>M) matrix, c the unknown coefficients and y... Aug21-14 03:11 PM mfb 9 521 I am somewhat confused with the connection between the two groups. In the text I'm reading (An Introduction to... Aug21-14 11:00 AM HomogenousCow 7 340 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 6 313 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 3 415 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 10 481 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!" 2 300 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 3 254 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 2 461 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 1 443 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 1 452 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 3 292 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 1 273 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 3 284 Why do we need fields (Why do we define fields?)for linear algebra? Aug14-14 12:45 AM homeomorphic 10 360 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 10 422 (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 2 434 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 2 325 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 2 877 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 1 417 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 3 493 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 2 399 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 6 422 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 17 754 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 3 505 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 2,000 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 2 435 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 10 687 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 15 885