# Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
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 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 28,414 Hello, I am reading a set of lecture notes on lattice QCD:... Sep26-12 10:58 AM evilcman 0 437 Let x be in R^n and Q in Mat(R,n) where Q is hermitian and negative definite. Let (.,.) be the usual euclidian inner... Jul17-12 02:09 PM micromass 1 640 Sorry for not being very descriptive in the title, but here's my problem: Prove that for all a,b,c,d \ge 0, the... Apr6-10 06:59 PM Tobias Funke 9 4,188 is there some theorem of some sort, that connect the number of divisors of a number to identify if it's even or odd? ... Apr2-06 01:47 PM Gokul43201 4 2,723 prove that there are infinetely many primes of the form 3n+1 we used : Assume there is a finitely # of primes... Jan25-05 12:10 PM shmoe 4 3,092 Ok I understand the concept of infinite countability and that say the set of all rational #s is infinitely countable,... Nov27-12 06:43 PM Mark44 1 1,422 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 0 312 I'm currently going through Hungerford's book "Algebra", and the first proof I found a bit confusing is the proof of... Aug2-08 04:42 AM radou 9 4,621 I'm trying to understand this paper which the author claimed that he had constructed an infinite dimensional... Apr6-09 02:06 AM matematikawan 6 1,578 Can you guys provide a counter example of why this statement is False. If T: V-->V with V a VS over C then T has an... Nov7-10 08:18 AM Landau 1 1,002 According to my professor, there exist infinite dimensional vector spaces without a basis, and he asked us to find... Oct23-12 02:27 PM Vargo 5 1,588 Can anyone think of an example of an infinite group that has elements with a finite order? Oct5-11 06:00 AM Bacle 10 3,472 I am a computer scientist that only recently got interested in topology. I have got the following question: How to... Feb4-06 01:03 PM HallsofIvy 18 2,949 How do you find an infinite number of units of \mathbb{Q}(\sqrt{21}) using the \sqrt(21)? I saw one example using... May7-11 04:31 PM math_grl 4 1,761 Ok, here is the situation. I am working on a take home in which I have this problem involving the order of a group. ... Apr19-04 04:39 PM Wrench 4 2,748 Someone told me Euler proved that there are infinitely many prime numbers by proving that the sum of their reciprocals... Mar11-12 10:47 AM MostlyConfusd 2 1,058 I've been able to prove that the set {8n+7} has infinite primes by manipulating Fermat's Theorem, but I'm trying to... Dec12-05 01:38 AM shmoe 1 2,402 hello guys . question here how can i prove that there exists infinitely many primes p such that p = 3 mod 4. i... Dec10-07 02:24 PM al-mahed 8 4,378 work out the value of the following: :redface: 1/2*sqrtsqrt]... Any help is appreciated. :confused: :smile:... Jun19-04 12:45 AM geraldmcgarvey 13 2,582 ?=\prod_{n=1}^\infty(n/(n+1)) Sep16-09 11:02 PM Loren Booda 3 1,398 Hey! Is there an infinite ring with exactly two maximal ideals. Thanks in advance LiKeMath Dec19-12 12:29 PM mathwonk 4 990 A while back I posted a question about this series on the General Math forum and was brought to task for not showing... Apr8-11 05:40 PM Raphie 3 1,936 Infinite Set ( 1 2) Let G be a finite nonempty set with an operation * such that: 1. G is closed under *. 2. * is associative. 3.... Jul14-08 04:16 PM matt grime 29 3,188 Could someone explain the following theorem to me: Given a homogeneous system of n linear equations in m... Sep6-12 08:55 AM HallsofIvy 2 1,690 I've been trying to simplify a formula that looks something like this: X = \sum_{k=0}^{\infty} v_{x} v_{y} where... Jan16-10 07:51 PM diazona 0 863 May be someone following this section may help me, see this thread:... Aug5-10 09:14 AM Goldbeetle 0 984 I have been working with the following series $\sum_{n=0}^\infty \frac{x^n}{a+x^n}$, where \$00 n*phi(n)=k! (phi is Euler totient) Are there infinitely many solutions ? The first few solutions ... Mar12-12 04:55 PM Gaussianheart 5 1,328 What's an example of a group that has finitely many generators, but cannot be presented using only finitely many... Sep4-12 10:54 PM DonAntonio 1 780 I've already post this, but i've done it in the wrong section!! So here I go again.. I've a doubt on the way the... Jun28-11 09:44 AM teddd 12 2,637 Is there any method to show that their are infinitley many prime numbers? May25-11 02:49 AM Borek 6 1,180 Infinity ( 1 2) x + x = 2x infinity + infinity = 2 infinity (or) infinity x-x=0 infinity * infinity = square of infinity (or)... Mar21-05 05:35 PM phoenixthoth 24 4,981 I've heard, and agree, that infinity (I) divided by 0 is impossible, yet somewhere I saw that I/0 * 0/I = 1 is this... Apr14-05 07:50 PM Hurkyl 14 2,725

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