# Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
 Views: 224 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 28,503 Hi all, I have a linear algebra question relating actually to control systems (applied differential equations) ... Nov16-12 10:07 AM X89codered89X 1 685 So I was working through some problems in Herstein's Algebra on my own time, and I came across something I wasn't so... Nov16-12 12:00 AM mathwonk 8 1,654 Let k\in\mathbb{N}, and q be a prime factor of F_{k}=2^{2^{k}}+1. Deduce that gcd(q-1,2^{k+1})=2^{k+1}. ... Nov15-12 12:49 PM TaliskerBA 1 1,333 I need help or direction on how to prove that if A = S^2 - (T^2 + T)/2 Then 8A-1 can not be factored into the form B*C... Nov15-12 08:41 AM Norwegian 4 1,606 Is there one? I know A= and A-1= So I know that A and A-1 have the same eigenvalues, I know that this is not... Nov14-12 05:57 PM BrainHurts 7 1,156 Hi, Algebraists: Say V is finite-dimensional over F . Is there more than one way of defining the action of F on... Nov14-12 05:19 PM Erland 1 707 Suppose that M and N are natural numbers, such that N>M-1. Prove that N≥M The problem above is a rather minor... Nov14-12 10:28 AM Vargo 6 1,511 Hey! I have a certain problem. Let M ≥ 4 be an even number and consider the set \frac{M}{2}-1]. The problem is to... Nov13-12 01:36 PM Constantinos 0 694 I am wondering about the relation betwen RRE forms and identity matrices. Consider the reduced row echelon form of any... Nov13-12 11:00 AM Erland 8 1,211 The Cantor-Schreuder-Berstien theorem states that if there exists a one-to-one function from X to Y and the reverse... Nov13-12 03:42 AM micromass 4 744 What is the best way of introducing determinants on a linear algebra course? I want to give real life examples of... Nov12-12 10:31 PM mathwonk 3 792 I am trying to understand the quantum algorithm for order finding, but I can't find the proof anywhere. Can anyone... Nov12-12 09:18 PM jhendren 1 1,140 So I've been reading a bit about automorphisms today and I was wondering about something. I'm particularly talking... Nov12-12 09:12 PM Zondrina 6 817 the polynomial x^4+8x+12=0 has the Galois group A4. I have all its roots, but can't figure out its splitting field. ... Nov12-12 07:55 PM Jim Kata 7 942 Hi, this is not a homework problem, i just have a hard time following the sequence of this In the book , it shows a... Nov12-12 06:50 PM mickles 4 1,300 Hi, I need help in the following demonstration: If (m,n)=d then \Phi(mn)=\frac{d}{\Phi(d)}\Phi(m)\Phi(n) ... Nov12-12 06:04 PM PiAreSquared 1 994 I'm trying to understand a process called order finding as I need to know it for Shor's algorithm in quantum... Nov12-12 04:31 PM Erland 2 1,429 Consider θ:Z -> Z is a mapping where θ(n) = n^3 and it's homomorphism under multiplication. In this case, it's not a... Nov12-12 03:28 PM Turnyface 9 730 Hello everybody I have to show that this set of vectors a = (e-t, e-it, et, eit ) is linearly independent. My... Nov12-12 01:08 PM Vargo 2 878 Hi, All: Let V be a finite-dimensional space, which can be decomposed as: V=Z(+)W . How can we express the... Nov12-12 12:53 PM Vargo 1 617 I understand how to find an implicit description if given the span of, say, two vectors. How do I go about finding an... Nov11-12 12:38 PM hogrampage 4 930 f(x) will give us the smallest integer m such that y^m \equiv 1 \bmod{x} given that x and y are coprime how would... Nov11-12 06:30 AM dodo 6 1,872 I can't seem to make head or tail of the description of direct and inverse limits of abelian groups in problems 8 and... Nov10-12 08:47 PM mathwonk 2 848 How should one prove that the integers form a commutative ring? Im not sure exactly where to go with this and how much... Nov10-12 04:22 PM Square1 2 796 My prof uses this all over his notes, and I'm still not 100% sure what he means by it: CB or BB From what... Nov10-12 03:15 PM Stephen Tashi 1 579 I was wondering if there are any theorems that specify an exact number of subgroups that a group G has, maybe given... Nov9-12 03:42 PM Vargo 1 788 As part of a larger problem involving classifying intertwining operators of two group representations, I came across... Nov8-12 02:54 PM Vargo 2 923 Ok, so I understand that a vector space is basically the span of a set of vectors (i.e.) all the possible linear... Nov8-12 02:51 PM Vargo 9 849 Hi, I want to whether there is a function (/matrix) such that it can generate a m-dimensional vector such that this... Nov8-12 09:13 AM mathwonk 1 868 Very much a beginner in maths and broadening my horizons. I have a series of polynomials that I was hoping to get some... Nov8-12 05:11 AM Guffel 1 1,496 I can't figure out how to simplify the equation E2=m2c4+p2c2 to Emγc2! This is driving me crazy trying to! How do you? Nov7-12 02:49 PM micromass 2 1,009 Consider the system of linear equations (A+D)x=b, where D is a positive semidefinite diagonal matrix. Assume for... Nov6-12 06:03 PM JohnSimpson 0 515 Hi i have two questions regarding this definition: "A vector space is a set that is closed under finite vector... Nov6-12 02:27 PM christian0710 5 793 Say I have a set of points in 2D space. How would I find a line that maximizes the sum orthogonal projection of the... Nov6-12 11:08 AM mfb 11 960 So I want to clarify if what I'm thinking is correct. Suppose we have a mapping f : A → B and we have a in A and b... Nov5-12 05:21 PM micromass 4 608 I don't know how to write out matrices nicely on this forum, but suppose you have some matrices: This... Nov5-12 02:54 PM micromass 1 620 How do you construct a group that is a non-trivial (not a direct product) extension of a two dimensional free abelian... Nov5-12 10:44 AM lavinia 0 596 I'm making notes for linear algebra, and I'm using the weaker definition for the invertible matrix: "A matrix A is... Nov5-12 01:31 AM mathwonk 3 749 Does any circle having irrational radius have no lattice points on its boundary ? Extended question: Is there any way... Nov5-12 12:02 AM funcalys 6 1,492 Hello guise. I am familiar to a method of diagonalizing an nxn-matrix which fulfills the following condition: the... Nov4-12 09:32 PM divergentgrad 10 1,313