# 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: 5,345 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 36,230 Is the derivative operator d/dx bounded with respect to the norm defined by integral from 0 to 1 of f g*... Nov14-09 01:01 PM esisk 2 1,313 hi can someone tell me...how to correctly use the 10 axioms.. for example: does the set of all 3x3 symmetric matrices... Nov14-09 04:11 AM HallsofIvy 3 2,637 I'm going to be doing research next semester on a topic of almost entirely my choice. I'd like to research anything... Nov13-09 03:07 PM Newtime 3 1,678 First, sorry for my poor English and any impolite behavior might happen. Here's two wave function(pic1) and problem... Nov13-09 07:56 AM boladore 0 2,903 I'm trying to show that a set W of polynomials in P2 such that p(1)=0 is a subspace of P2. Then find a basis for W... Nov13-09 06:00 AM HallsofIvy 11 4,777 The question posed is "Classify up to similarity all 3 x 3 complex matrices A s.t. A^{3} = I. I think the biggest... Nov11-09 09:17 AM g_edgar 4 2,537 Hi, I've been trying to show that the set of matrices that preserve L1 norm (sum of absolute values of each... Nov11-09 09:11 AM g_edgar 5 3,307 I'm looking at the exercises of Hungerfod's Algebra. Some looks easy but it seems the proofs are not so obvious.... Nov11-09 12:27 AM Spartan Math 4 7,282 i)]+1=0 :I had a friend with a T-shirt displaying this deceptively simple equation. I know it to be true, but I have... Nov10-09 06:23 AM widewombat 51 23,597 can explain to me what is mean of span? from book, it say "every vector in the space can be expressed as linear... Nov10-09 01:02 AM Dafe 6 1,611 If I have a matrix A, and I use n different row operations of this form: a_kR_i + R_j \rightarrow R_i to construct a... Nov9-09 08:01 PM slider142 5 1,040 The positive powers of 2 mod 5^m cycle with period 4*5^(m-1), which you can prove by showing that 2 is a primitive... Nov9-09 10:59 AM DoctorBinary 8 5,255 Let E = span{v1, v2} be the linear subspace of R3 spanned by the vectors v1 = (0,1,-2) and v2 = (1, 1, 1). Find... Nov8-09 09:12 PM epkid08 8 3,341 Suppose that a casino introduces a game in which a player bets $1 and can either win$2 or lose it, both with equal... Nov8-09 02:39 AM ha9981 0 2,078 I am working on some homework that I already handed in, but I cant get one of the problems. The fourth problem on the... Nov7-09 11:46 AM prez 3 6,010 Hi, I am trying to verify with anybody generally intrigued by the Riemann Hypothesis whether they might find of any... Nov7-09 05:14 AM Luca 0 1,355 Let's say I have a matrix A: A=\begin{bmatrix} f(x)& z_1(x)& z_2(x)\\ 0& a(x)& b(x)\\ 0& c(x)& d(x) ... Nov6-09 09:24 PM HallsofIvy 9 1,195 I did a problem in class today that evaluated f(t)=e^{At} for A_{2,2}=\begin{bmatrix}2&1 \\-1&4 \end{bmatrix} to a... Nov6-09 04:30 PM tiny-tim 1 880 right now, my concept for their difference is that linear transformations are 1 to 1, where as nonlinear... Nov5-09 04:04 AM HallsofIvy 2 10,313 I had a question about the following theorem. Basis Representation Theorem: Let k be any integer larger than 1. ... Nov5-09 02:12 AM ppd 3 6,418 Suppose A is a finite abelian group and p is a prime. A^p={a^p : a in A} and A_p={x:x^p=1,x in A}. How to show A/A^p... Nov4-09 04:33 PM ilia1987 1 2,248 Hi, I'm applying the Lanczos algorithm to find the minimal eigenvalue of some huge matrix. Now that I've got it I'm... Nov3-09 01:06 PM maverick_starstrider 0 1,890 What would be a formula for determining an estimate of a track runner's speed in comparison to other racers before... Nov3-09 12:16 PM bobbobwhite 0 618 For example, if alpha = 1, there is an unqiue solution. then what value(s) of alpha will make the system... Nov3-09 09:05 AM ZannX 2 5,543 I have a system of linear equations which can be expressed as XA=Y where X and Y are row vectors. The vector Y and the... Nov3-09 08:42 AM ZannX 5 2,310 Hi all, so I was looking at Legendre symbols, and I saw that \left(\frac{2}{p}\right)=(-1)^{\frac{p^2-1}{8}}. ... Nov3-09 02:23 AM thomas430 5 3,065 Hi all I am looking for a way of estimating stress and displacement of the following frame. I used ANSYS to analyze... Nov2-09 12:51 PM srosendal 0 5,818 Im trying to prove N(N(P)) = N(P) So N(P) = set oh h where h^-1Ph = p Then N(N(P)) = k where k^-1hk = h the... Nov2-09 11:18 AM Niall101 4 1,909 Let the vectors a1,a2,a3 €R3 and b1,b2,b3 € R4 be given by a1 a2 a3 1 -2 3 2 2 1 ... Nov2-09 05:28 AM orange12 3 919 given the function Z(s)= \prod _{k=0}^{\infty}\zeta (s+k) with \zeta (s) being the Riemann Zeta function the... Nov1-09 06:08 PM Petek 3 2,036 Hey. Got some troubles with this. 4 1 11 A= 1 3 11 0 2 6 ... Nov1-09 05:08 PM orange12 3 1,041 First off I am NOT asking you to solve this for me. I'm just trying to understand the concept behind this problem. ... Oct31-09 05:35 PM HallsofIvy 14 2,429 I have been working on integer factorization with pq = n and have written a paper on the special case for q < 2p. I... Oct31-09 06:10 AM mgb777 0 1,298 Let A_i (i=1,...,k) be a nonsingular complex matrix which size is M by M. The question is how to find a complex... Oct31-09 03:11 AM HallsofIvy 1 1,014 There are square pyramidal numbers and tetrahedral numbers, defined Square pyramidal numbers = n ( n + 1 )( 2 n +... Oct30-09 01:52 PM CRGreathouse 6 4,206 Hi, I'm not sure to which forum my question related. Is there a connection between models used in mathematics of... Oct30-09 10:59 AM yaron123 0 2,659 Hi, For a given problem, A*X = B where A is a NxN matrix, X and B are Nx1 accordingly, I understand that a poor... Oct29-09 01:12 PM ZannX 0 1,718 can u help me with this question If n ≥ 6 is a composite integer, then n |(n − 1)! If n is a prime number, then n... Oct29-09 07:04 AM Bingk 6 1,329 Hello, If we are given that b3|a2, how do we show that b|a? I started off looking at prime factorizations, but I... Oct29-09 06:41 AM Bingk 6 1,331 This is my first post on the physicsforums so go easy on me :) I am writing a simple program to generate the zero's... Oct29-09 04:38 AM marcusmath 2 3,108