# 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 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 30,487 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 2 397 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 4 397 Exist so much theory for find the eigenvules of a matrix (invariants, characteristic polynomials, algebraic formula... Feb24-14 01:57 PM DrClaude 4 397 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 2 398 Hi everyone, I have a square matrix J \in \mathbb{C}^{2n \times 2n}... Feb27-14 11:57 AM Sam1984 0 398 I have begun to learn about maximal elements from a linear algebraic perspective (maximal linearly independent subsets... Jun13-13 06:58 AM HallsofIvy 1 399 Is any given finite semigroup isomorphic to some finite semigroup S that consists of some subsets of some finite group... Jul24-13 07:13 PM micromass 4 401 In a linear regression with 1 independent variable, if X is always the same (let's call I am unlucky), but Y present... Jun26-13 03:57 PM Number Nine 2 402 Hi everyone, I would like to ask you something about vector spaces. I have the following term: S=dim(R(... Aug2-13 10:19 AM GoodSpirit 0 403 Here it is for those interested. http://arxiv.org/pdf/1305.2897.pdf May28-13 08:47 AM epsi00 0 404 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 12:19 PM mathsciguy 2 404 Hi, Could anyone give me a proof for the following theorem? Theorem : Ax=0 has a non-trivial solution iff det(A)=0... Mar27-14 06:47 AM chogg 2 404 In "Quantum Computation and Quantum Information" by Nielsen & Chuang, on pp. 88-89, applying basic statistical... Mar19-14 04:06 AM nomadreid 2 406 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 06:12 AM Kosh Naranek 1 408 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 2 408 http://img826.imageshack.us/img826/6069/kj13.png The proof is showing that particular matrix ring is not left... Oct27-13 11:10 AM Silversonic 0 408 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 02:01 PM vnikoofard 0 411 Suppose I have some functions ## \{ y,y_{1},y_{2},...y_{n} \} \subset C^{∞} ## and suppose I know that the Wronskian... Jul30-13 12:42 PM Mandelbroth 1 412 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 09:37 AM R136a1 1 412 Hi guys, So as title states, how would one sketch Re(iz) = 3? And an explanation would be splendid. This is what I... Feb6-14 09:35 PM JC3187 5 412 Friedberg proves the following theorem: Let V and W be vector spaces over a common field F, and suppose that V is... Jun10-13 12:25 PM micromass 1 413 Hello! I ve come across with something called ' relative element of a vector' Could you provide me a definition and... Jul25-13 04:27 PM Stephen Tashi 1 413 Hi all, Im trying to think of a way of generating non-intersecting randomly oriented cylinders within a unit cell... Feb12-14 07:06 AM FactChecker 9 413 I was developing a pythagorean theorem proof based on the cross product of two vectors..Below is my final... Feb1-14 09:03 PM FactChecker 3 414 When I start to read the the article called "symmetric bi-linear forms", I face the following sentence. But I don't... Aug4-13 11:49 PM micromass 3 415 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 2 416 Let's say we randomly select integers to construct a potentially infinite number, for example 3588945.... There is a... Apr4-14 12:59 PM SteveL27 2 416 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 05:18 AM Fredrik 5 417 delete please Feb6-14 02:24 PM pasmith 1 417 Using the given information, is it possible to solve the new travel direction of the smiley face? To clarify, I am... May29-13 06:48 PM Simon Bridge 6 418 I have some reason to believe that \det(\textrm{id} + AB) = \det(\textrm{id} + BA) is true even when AB and... Jun20-13 10:47 PM jostpuur 2 418 For another thread http://www.physicsforums.com/showthread.php?p=4420542 , I want to give simple motivations for the... Jun23-13 01:19 AM Stephen Tashi 3 418 I was having a quick look at Isaacs : Algebra - A Graduate Course and was interested in his approach to Noetherian... Oct31-13 01:02 AM R136a1 3 418 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 07:14 AM Jeff.Nevington 2 418 For a linear transformation to be invertible, is it a requirement that the domain and codomain be the same vector... Jun11-13 08:26 AM HallsofIvy 3 419 Hi, I'm getting a bit confused about the adjoint representation. I learnt about Lie algrebras using the book by... Aug2-13 03:24 PM AlbertEi 0 419 0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0 is a short exact sequence if the image of any morphism is the... Dec12-13 01:07 PM gentsagree 2 419 Hi all! I have no application in mind for the following question but it find it curious to think about: Say that... May31-13 06:43 PM mfb 1 420 Using this coordinate system and writing the relationships: \vec{\rho}\;'=R^{-1}(\phi)\vec{\rho} \begin{bmatrix}... Jan27-14 09:18 AM Jhenrique 2 421 Not sure if this is the right subforum. This is technically a signal processing question, but it edges on proving... Apr7-14 11:24 AM jbunniii 12 421