# 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: 76,232 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 How to detect redundant equation from a system of nonlinear equation? It means how to find out a system of nonlinear... May26-12 06:02 AM algebrat 3 2,583 Are there any nice applications of the Cayley Hamilton Theorem. I am looking for a real life application which would... Jun22-12 02:08 AM marygoss 3 11,173 Consider the space of all polynomials in n variables of degree at most d. The dimension of that space is C(n+d,d). How... Jul15-12 06:29 AM chiro 3 2,439 I am wondering how to organise all of those concepts in my head. should i think of it like: subspace > vectorspace... May26-12 08:12 AM algebrat 3 1,502 Hi: I am a newbie to linear algebra; I have a problem about vector space and subspaces. How to distinguish these... May17-12 05:44 PM applechu 3 1,024 Hello, The formulation of the question says: Show, using congruences and disjunction of cases, which,for all... May17-12 08:09 PM ramsey2879 3 2,149 Is it correct to say that any order 4 group is only isomorphic to either C4 or C2+C2 ? where C4 is the order 4... May23-12 03:10 PM lpetrich 3 1,713 There is a difference between the multiplication op in the Field of Reals and the Scaling op in the Set of Vectors. In... May23-12 04:57 PM SteveL27 3 1,402 good day! i need to prove that the alternating group An is a normal subgroup of symmetric group, Sn, and i just want... May26-12 07:34 PM haruspex 3 1,156 I'm doing a particular form of regression that gives a eigenvector and matrix for the solution. I'm using two matrix... May31-12 08:51 PM chiro 3 1,250 Ok, to start off I have been examining the structure of polynomials. For instance, consider the general polynomial ... Jun1-12 02:38 PM galoisjr 3 1,234 i'm trying to find a version of PARI or PARI/GP or a comparable number theory program that will run on my MacBook Pro.... Jun16-12 01:19 AM TylerH 3 2,119 What is the LaTex and infinite sum for 1-2-1/2+3-1/2-4-1/2+5-1/2 . . . Does it converge anyway? I am too old for... Jun5-12 04:16 AM Xitami 3 2,137 Show that a rotation by θ followed by a rotation by φ can be expressed as either two consecutive rotations, or one... Jun13-12 03:47 PM HallsofIvy 3 1,266 Is there such a thing as a "feral polynomial" ? Saw it mentioned on an Internet forum where someone claimed to be... Jun16-12 11:52 AM HallsofIvy 3 964 Here's a question. Pi is said to be the ratio of a circle's circumference to its diameter. If this is the case, what... Jun21-12 08:23 PM SteveL27 3 2,248 I'm reading through a multivariable calculus book and it starts off with some linear algebra. It defines vector... Jun23-12 07:29 PM jcsd 3 1,398 Exercise #17 in Linear Algebra done right is to prove that the dimension of the direct sum of subspaces of V is equal... Jun25-12 01:02 PM DonAntonio 3 1,357 Hello, I am looking at the proof (Theorem 2.5 (b) Apostol) of $$\phi (mn) = \phi(m) \phi(n) \frac{d}{\phi(d)}$$... Jun28-12 06:03 PM DonAntonio 3 1,745 Assume u:R\rightarrow C^n and define shift operator S(\tau) with S(\tau)u(t)=u(t-\tau) and truncation operator... Jul1-12 02:58 AM Einj 3 902 Proposition: \sum_{i=0}^{p-1} (\frac{i^2+a}{p})=-1 for any odd prime p and any integer a. (I am referring to the... Jul2-12 04:21 PM DonAntonio 3 1,638 I have a large real symmetric square matrix (with millions of rows/columns). How can I identify the sets of rows that... Jul18-12 10:26 AM Big Data Alan 3 1,732 Disclaimer: Sorry if this question is off-topic, I really don't yet know where it "belongs". I wrote a program that... Jul7-12 03:22 PM matthew180 3 1,283 For approximately the last two years, I have been working off and on for a proof of whether Brocard's problem was... Jul9-12 02:25 PM Millennial 3 2,449 Can someone please explain why 80 mod (-11) is -8…? Why isn’t it 3? b = aq + r 80 = (-11)q + r 80 = (-11)(-7) + 3... Jul15-12 08:25 AM HallsofIvy 3 1,642 I'm self-studying representation theory for finite groups using "Group Theory and Quantum Mechanics" by Michael... Jul19-12 04:27 PM LastOneStanding 3 1,152 Say we complex structure J on a space with even dimension. Is there a trick to finding another complex stucture I that... Jul24-12 09:04 PM Ben Niehoff 3 961 Def: A low discrepancy sequence is a uniformly distributed sequence with minimal discrepancy, O(logN/N). Question:... Aug2-12 03:26 PM mehr1methanol 3 1,380 Suppose that we have a cross-product of vectors. a × b = c Now suppose that we have an orthogonal matrix M. Is... Jul23-12 07:16 PM micromass 3 1,817 Say I have a system of equations of the following form: a_1 A^2 + b_1 B^2 + c_1 C^2 + d_1 = f_1 a_2 A^2 + b_2 B^2... Jul27-12 06:56 AM HallsofIvy 3 851 Assume P is a symmetric positive-definite matrix, and S to be a diagonal matrix with all its diagonal elements being... Aug1-12 02:26 AM chiro 3 1,204 I am having trouble understanding the permutations of a finite set in general. I want to know what it may be used for,... Aug3-12 01:59 PM marschmellow 3 1,120 Hello everyone, this nxn matrix arises in my numerical scheme for solving a diffusion PDE. M =... Aug1-12 09:09 AM Jonnyb302 3 888 Let us take the most mainstream irrational out there, (Pi). Now write (Pi) as: 3. 14159265... Let us number... Aug5-12 07:34 AM mfb 3 1,783 This is very weird, but I found an inconsistency in the application of Cramer's Rule for a 3x3 simple linear matrix. ... Aug10-12 10:03 AM DonAntonio 3 1,019 Suppose we have a finite dimensional inner product space V over the field F. We can define a map from V to F... Aug11-12 08:13 PM dEdt 3 1,215 The isomorphism of ℝ5 and P4 is obvious for the "standard" inner product space. The following question arise from... Aug18-12 09:58 PM chiro 3 1,039 Can any one clarify the concepts of zero vector and zero scalar? -Devanand T Aug18-12 10:13 AM Fredrik 3 2,248 Hello fellas. I have this formula that encodes data: OUTPUT = (Data * 7) + (Data * 2) + 8 So in this case, if... Aug14-12 06:11 AM chiro 3 793 Let p be a prime. Let H_{i}, i=1,...,n be normal subgroups of a finite group G. I want to prove the following: If... Aug16-12 10:10 PM moont14263 3 1,139