# 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: 76,235 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 33,911 What is the infinite product for the function \Xi(s)=\Gamma\left(\frac{s}{2}\right)\pi^{-s/2}\zeta(s) ? Feb17-10 07:52 PM Charles49 3 3,395 Here is an interesting problem that I've been thinking about for a while: Let p be a prime s.t. p = 4m+1 for some... Feb1-10 10:12 AM joeblow 3 3,834 Hello. I have been reading a book with an introductory section on number theory and the part regarding Euler's... Jan22-10 12:22 PM dodo 3 2,500 From this example Anti-Aliasing section 22.4.1 http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter22.html... Jan26-10 10:56 AM rebeka 3 1,783 Hi Folks, I have a question about determinants that is probably quite simple. I know that if you have a matrix and... Jan27-10 09:32 AM ulriksvensson 3 967 I wonder if all coupling set of equations are not solvable analytically? I have a equation set as follows y1 =... Jan27-10 12:07 PM B-Con 3 1,264 Hello dear forum member I wanted to know how about the research on this branch of science.Are many people working on... Jan31-10 06:06 AM zetafunction 3 2,181 Hi, I have just started teaching linear algebra to myself. I know nothing about linear algebra so if this question... Feb3-10 06:50 PM Zaphos 3 2,947 Hey everyone, I'm taking this course called "Number Theory" and am having a lot of difficulty with it. We're... Feb2-10 10:38 PM ramsey2879 3 1,656 Hi, I am new with linear algebra, and I'm having a hard time wrapping my mind around the 0 vector and the additive... Feb2-10 07:40 AM radou 3 1,858 I recently teach myself linear algebra with Friedberg's textbook. And I have a question about adjoint operator, which... Feb4-10 06:04 AM typhoonss821 3 1,154 hi. i'm reading "quantum mechanics in hilbert space" and a don't get a basic point for bounded operators. def. 1... Feb10-10 07:25 AM tommy01 3 933 Clearly I am missing something obvious here, but how is it that negative even numbers are zeros of the Riemann zeta... Feb10-10 12:10 PM mrbohn1 3 4,524 Hello math goers, My education in linear algebra is limited to an Intro course I took a year ago. So I am posting... Apr12-10 05:34 PM Xuser 3 1,165 G group, H subgroup of G. Suppose aH and bH are distinct leftcosets then Ha and Hb must be distinct right cosets? ... Feb16-10 08:25 PM Fredrik 3 2,771 "Let m and k be positive integers and φ(m) is the Euler's phi function. Then the number of integers n such that 1≤n≤mk... Feb21-10 04:31 PM CRGreathouse 3 1,634 I'm a physics major. As such, I have come across several situations in my studies that require the use of eigenvectors... Feb22-10 09:04 AM imaloonru 3 1,793 4=2+2, 6=3+3. Are there any other cases where an even number of the form 2p, where p is a prime, cannot be... Feb22-10 05:20 PM CRGreathouse 3 1,841 I am having trouble understanding this example: Let G=S_3 and H={(1),(13)}. Then the left cosets of H in G are ... Feb25-10 02:32 AM mrbohn1 3 1,040 Show that (p-1)(p-2)...(p-r)==(-1)^r*r!(mod p) for r=1, 2, ..., p-1. I am having trouble getting this proof started.... Feb24-10 03:38 PM Tinyboss 3 1,878 1) Definition: Let m denote a positive integer and a any integer such that gcd(a,m)=1. Let h be the smallest positive... Mar1-10 09:49 PM VeeEight 3 1,942 Hello there, I have trouble understanding why the coefficients in an affine combination should add up to 1; From... Mar9-10 04:17 AM mrbohn1 3 2,532 given the sequence (power series) g(x)= \sum_{n\ge 0}a(n)(-1)^{n}x^{n} if i define ... Mar14-10 01:42 PM g_edgar 3 1,287 How do we show that, given a matrix $A$, the sign of the determinant is positive or negative depending on the... Mar20-10 08:44 PM quasar987 3 1,056 G,H be groups(finite or infinite) Prove that if (G:H)=n, then there exist some normal subgroup K of G (G:K)≤n!... Mar22-10 08:23 AM emptyboat 3 1,188 Let f, g \in \mathbb{Z} be given as follows: f = x^8 + y^8 + z^6 and g = x^3 +y^3 + z^3. Express if possible f and g... Apr6-10 04:51 AM Eynstone 3 1,725 Can anyone explain, in detail, why/why not Z/(2x) is isomorphic to Z/2Z? I know that every element in Z can be written... Mar30-10 09:01 AM eok20 3 2,673 I have seen that there exists two group homomorphisms from Z to Z/2Z. However, I cannot seem to understand this. I... Mar31-10 05:20 PM Landau 3 1,778 How can we find the determinant of a complex matrix? Apr1-10 07:11 AM HallsofIvy 3 5,811 I have a pretty basic question about direct sum/product of groups. Say you were given the group (Z4 x Z2, +mod2).... Apr5-10 12:20 AM shallumstuart 3 2,882 My best guess is this fits in algebra, I've been scratching my head with this for a while. I have a three... Apr11-10 01:53 PM Live2Learn 3 1,705 Ok so I've been working on this problem and I'm really having some struggles grasping it. Here it is: Let W be... Apr11-10 11:45 PM Bacle 3 1,030 Hi, can anyone explain to me if a 3 x 4 matrix can have independent columns? How about independent rows? Thanks! Apr13-10 05:52 PM VeeEight 3 1,267 I have to linear equations 3x + 2y =7 and -6x + 6y= 6 when expressed as linear combination in column vector form... May14-10 04:33 PM Noxide 3 1,353 Hi, I'm reading Shankar's Principles of QM and I find it not very clear on how exactly should I change basis of... Apr28-10 09:23 PM Fredrik 3 1,545 One of the topics in my linear algebra course is kernel and range of a linear transformation. I have a firm... Apr21-10 12:55 AM radou 3 1,400 http://img710.imageshack.us/img710/2314/booleanalgebra.jpg AFAIK logic is all about "T"/"F" or 0/1, and boolean... Apr26-10 02:14 PM Tac-Tics 3 1,001 Let S be a set on which a linear order <= (less or equal) , is defined. Show that a non-empty finite subset has a max. Apr28-10 05:17 AM Martin Rattigan 3 832 Let A be an n x n matrix with eigenvalue \lambda . Prove that \lambda ^2 is and eigenvalue of A^2 and that if v is an... Apr29-10 08:53 PM Evo 3 859 First what are Idempotents? Second, If A and B are simliar matrices, show that if A is idempotent then so is B. May5-10 09:38 AM Landau 3 1,017