# Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
 Views: 276 Announcement: End of year contest, $75+$50 prize! Dec18-13 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 28,505 I was a bit confused the last paragraph before "Corollary 4.6.4". It says that we have the isomorphism \alpha : Z_k... Mar23-13 09:21 AM Artusartos 2 675 Hello, I'm in an introductory course about quantum computing. My math experience is fairly solid, but not very... Mar22-13 09:01 PM Ocifer 2 491 Good afternoon! I am working on a problem, where I at some point have to find the intersection between a polytope... Mar22-13 06:16 AM alsm 0 429 Let an,m be defined for the non-negative integers n and m such that n ≥ m. an,0 = 1 am,m = m! an+1,m+1 = (m+1)... Mar21-13 11:13 AM conquest 1 590 Hi everyone. Is there any way to set demands on least square solutions? I have an equation on the form Ax=b,... Mar21-13 08:59 AM Marvin_MKII 4 727 I think this may be a simple yes or no question. I am currently reading a book Vector and Tensor Analysis by... Mar20-13 04:49 PM atyy 4 1,069 Claim: If p \in R is irreducible and non-zero, then p is irreducible and prime in R Proof: Let I be the ideal... Mar20-13 04:44 PM jbunniii 1 453 it seems to have many different ways to express a determinant, when we are using indices to write vectors and tensors,... Mar20-13 12:45 AM chiro 1 460 Hello! If anybody has a minute, I'd appreciate a quick look-through of my proof that a finite abelian group can be... Mar18-13 03:37 AM jbunniii 4 733 Let A be any real invertible matrix. There exists a non-zero diagonal matrix D such that A^T D A=D. I'm pretty sure... Mar16-13 01:52 AM fzero 8 1,186 Consider an unbounded self-adjoint operator defined in a hilbert space(its domain isn't the entire hilbert space,of... Mar15-13 11:28 AM micromass 1 447 There is some theorem along the lines that any category of schemes embeds into a suitable Grothendieck topoi. What is... Mar15-13 03:45 AM Jim Kata 1 452 Hello ! I have an upper triangular matrix for an operator T in which an eigen value has been repeated s times in... Mar13-13 06:08 AM vish_maths 9 987 Hi all, Say that I already know W1, W2 are both subspaces of a vector space V, W1∩W2={0}, and that... Mar12-13 01:46 AM jbunniii 1 593 Hello, In my abstract algebra class, my teacher really stresses that when you show that a set is a group by... Mar11-13 07:14 PM Fredrik 3 564 Is there a nice way to show that Det(AB)=Det(A)Det(B) where A and B are n x n matrices over a commutative ring? I'm... Mar10-13 08:52 PM Bacle2 4 719 Hi! I was wondering why it is possible to write any proper orthochronous Lorentz transformation as an exponential... Mar10-13 01:42 PM wisvuze 7 928 I'm trying to find a way to simplify a complicated proof. The worst step of the proof involves a product of five 4×4... Mar10-13 07:36 AM Fredrik 2 590 There's this theorem: A linear map T: V→W is one-to-one iff Ker(T) = 0 I'm wondering if there's an analog for... Mar9-13 10:11 PM HallsofIvy 8 953 how do you prove the distributive quality of the cross and dot products? thanks very much! Mar9-13 05:37 AM mathnerd15 15 1,172 Hey everyone, im trying to figure this out, but no luck. Help would be much appreciated. So i am considering a... Mar9-13 04:50 AM jbunniii 2 459 Let q be a prime, k= q-2 and X be an Integer, I have found solutions for q=5,7,17 for the equation (2^k) - 7 = X^2... Mar9-13 04:45 AM Mickey1 12 3,802 Am i correct if I say that Fiedler number surges when percolation is at percolation threshold? Assume a randomly... Mar8-13 11:44 AM kosmos 0 394 To determine if a subset of a vector space is a subspace, it must be closed under addition and scalar multiplication. ... Mar7-13 08:36 PM MoreDrinks 2 489 I want somebody to help me what attempts have been made to understand the sequence of prime number. Is the Nth term of... Mar7-13 08:33 AM pedja 7 5,856 In texts about dirac delta,you often can find sentences like "The delta function is sometimes thought of as an... Mar6-13 03:57 PM mathman 4 525 a metric on the plane determines an action of SO(2) on is unit circle by rotation. Suppose one starts with a free... Mar5-13 12:28 PM Vargo 1 576 ^{}This may be a silly question, but if I have an 8x3 matrix X, for example, then the rows of this matrix will span R3... Mar4-13 08:37 PM chiro 1 593 I want a matrix W of size nxk (where n>>k) with the following two properties: 1. Sum of all elements of each row is... Mar3-13 11:01 PM AlephZero 1 501 Hi there all, I have a personal project I'm working on and since I haven't done any linear algebra in many years... Mar3-13 06:56 PM chiro 2 563 Even though this deals with programming an encryption algorithm I feel this is more math based so I'm asking it here.... Mar3-13 10:28 AM hackish 2 566 What is the most motivating way to introduce the sketching of conics which have a cross product terms? This topic... Mar1-13 04:48 PM Vargo 1 525 Hey I am really confused over free products. So I understand abstractly, I think. If we have two groups G, H,... Mar1-13 02:16 PM dumbQuestion 4 572 Hello everyone, I’d like to ask the following: Considering the matrices A and B, both with the dimensions n \times... Mar1-13 12:18 PM GoodSpirit 0 462 I am trying to prove that C\otimesC (taken over R) is equal to C^2. The method I have seen is to show the following... Mar1-13 09:35 AM Monobrow 0 525 Hey everyone first time poster here, I need help with some factoring of cubes. I know this might tie closely to... Feb27-13 05:34 PM JNeutron2186 2 735 Do you know where can I find proven identity det(AB)=det(A)det(B) using Levi Civita symbol. Feb26-13 09:44 PM micromass 1 592 Is it true that for any unital ring (not necessarily commutative), that we have a ring homomorphism for all a = (a_1,... Feb25-13 03:07 PM mathwonk 4 841 Can we compare matrices? If A-B>0 is positive definite, can we say A>B? Feb25-13 01:20 PM jbunniii 1 528 Firstly, I apologise if this is the wrong section, but as far as I could tell this was the most relevant. I have a... Feb25-13 08:09 AM Ziks 6 1,030