# Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
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 Views: 8,340 Announcement: Two free ways to get Gold Membership! Jan17-12 Meta Thread / Thread Starter Last Post Replies Views Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions... Feb23-13 10:24 AM micromass 1 29,788 The Fourier series can be used to represent an arbitrary function within the interval from - π to + π even though... Jun28-13 04:39 PM tiny-tim 1 365 I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and... Oct30-13 11:52 PM Math Amateur 2 365 Is there an algorithm which, given n, returns an integer x such that 2 has order n modulo x (i.e, 2^n = 1 mod x and n... Jan20-14 09:42 PM stroustroup 2 366 I was developing a pythagorean theorem proof based on the cross product of two vectors..Below is my final... Feb1-14 10:03 PM FactChecker 3 366 Is any given finite semigroup isomorphic to some finite semigroup S that consists of some subsets of some finite group... Jul24-13 08:13 PM micromass 4 367 Hello everyone: I have some question using the FFT in matlab for data interpolating. I don't know what the relation... Jul3-13 03:29 PM mathman 1 371 I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and... Oct31-13 12:54 AM Math Amateur 2 371 I have begun to learn about maximal elements from a linear algebraic perspective (maximal linearly independent subsets... Jun13-13 07:58 AM HallsofIvy 1 375 I am using linear regression to predict 'y' based on 8 variables. With my example, most the Betas that I got are... Jan29-14 11:58 PM FactChecker 4 375 Let's say I have a matrix M such that for vectors R and r in xy-coordinate system: R=Mr Suppose we diagonalized it... Jul24-13 01:19 PM mathsciguy 2 377 I'm looking for a way to construct a representation for a simple Lie group such that one particular subgroup is... Dec1-13 01:20 AM whitejet 0 377 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 04:33 PM AlephZero 2 380 For another thread http://www.physicsforums.com/showthread.php?p=4420542 , I want to give simple motivations for the... Jun23-13 02:19 AM Stephen Tashi 3 381 Here it is for those interested. http://arxiv.org/pdf/1305.2897.pdf May28-13 09:47 AM epsi00 0 382 Wasn't sure whether to post this in the computing section or not but here goes anyway, I have n number of 2d... Feb5-14 08:14 AM Jeff.Nevington 2 382 If I have two square nonnegative primitive matrices where the Perron-Frobenius Theorem applies how would I calculate... Jul4-13 10:01 PM Simon Bridge 2 383 Suppose I have some functions ## \{ y,y_{1},y_{2},...y_{n} \} \subset C^{∞} ## and suppose I know that the Wronskian... Jul30-13 01:42 PM Mandelbroth 1 383 Hi all, I'm testing out a matrix solving program and while it checks out for 2x2/3x3/4x4 I would like to try it out... Jun12-13 07:12 AM Kosh Naranek 1 385 Suppose we have $$=if^c_{ab}Q^c$$ where Q's are generators of a Lie algebra associated a SU(N) group. So Q's are... Jul24-13 03:01 PM vnikoofard 0 386 Hi everyone, I would like to ask you something about vector spaces. I have the following term: S=dim(R(... Aug2-13 11:19 AM GoodSpirit 0 388 Friedberg proves the following theorem: Let V and W be vector spaces over a common field F, and suppose that V is... Jun10-13 01:25 PM micromass 1 389 I am reading Dummit and Foote (D&F) Section 15.1 on Affine Algebraic Sets. On page 662 (see attached) D&F define a... Nov2-13 10:37 AM R136a1 1 389 http://img826.imageshack.us/img826/6069/kj13.png The proof is showing that particular matrix ring is not left... Oct27-13 12:10 PM Silversonic 0 390 Hi all! I have no application in mind for the following question but it find it curious to think about: Say that... May31-13 07:43 PM mfb 1 391 When I start to read the the article called "symmetric bi-linear forms", I face the following sentence. But I don't... Aug5-13 12:49 AM micromass 3 392 I have some question guys i have four points in the x,y plane in cartesian coordinates. A (Ax,Ay) B(Bx,By) ... Jun17-13 06:18 AM Fredrik 5 393 Hello! I ve come across with something called ' relative element of a vector' Could you provide me a definition and... Jul25-13 05:27 PM Stephen Tashi 1 393 I was having a quick look at Isaacs : Algebra - A Graduate Course and was interested in his approach to Noetherian... Oct31-13 02:02 AM R136a1 3 393 0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0 is a short exact sequence if the image of any morphism is the... Dec12-13 02:07 PM gentsagree 2 393 What is the basis of a bivector? For example (see the attachment and... Jan21-14 02:22 PM tiny-tim 3 394 Any comments or feedback on this theorem and proof are appreciated, including improvements and past publications. ... May8-13 02:32 AM THSMathWhiz 0 396 Hi, I'm getting a bit confused about the adjoint representation. I learnt about Lie algrebras using the book by... Aug2-13 04:24 PM AlbertEi 0 398 Using the given information, is it possible to solve the new travel direction of the smiley face? To clarify, I am... May29-13 07:48 PM Simon Bridge 6 399 I have some reason to believe that \det(\textrm{id} + AB) = \det(\textrm{id} + BA) is true even when AB and... Jun20-13 11:47 PM jostpuur 2 400 Hello. So today in class, we talked a bit about as the set of all integer powers of g. Made enough sense. Then we... Oct10-13 04:41 AM Convergence 1 400 For a linear transformation to be invertible, is it a requirement that the domain and codomain be the same vector... Jun11-13 09:26 AM HallsofIvy 3 401 If I want to show two orthogonal subsets S_{1} and S_{2} of ℝ^{n} both span the same subspace W of ℝ^{n} does it... Dec12-13 10:51 AM NATURE.M 4 401 Using this coordinate system and writing the relationships: \vec{\rho}\;'=R^{-1}(\phi)\vec{\rho} \begin{bmatrix}... Jan27-14 10:18 AM Jhenrique 2 401 Good morning, my name is Alberto and I'm from Peru (South America); and this is my first post on this forum. My... Dec11-13 07:56 AM jedishrfu 1 402 Dear All: For a line structure(say a very long atomic chain) and a closed loop structure( connect the head and tail... Nov1-13 09:30 AM HallsofIvy 4 405

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