# 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: 2,613 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 35,963 Hi this is my first post on this site and glad to be here! Ive only really started looking into maths and physics... Sep21-12 10:05 PM bahamagreen 5 2,090 Hello I'm reading my old notes of QM, I found the definition of Pauli vector, as follow \vec{\sigma}=\sigma_1... Sep18-12 10:42 AM dextercioby 4 2,107 Hey all, I am trying to get a head start on Linear Algebra before i start taking classes in a couple weeks. I am... Sep16-12 09:51 PM homeomorphic 10 5,477 Hello Forum, a system of linear equations can be determined (if there are as many unknowns as equations),... Sep17-12 10:56 AM fisico30 15 2,648 Consider the separation of the Riemann Zeta function in two terms \begin{flalign*} \zeta(s) &= 1^{-s} + 2^{-s} +... Sep19-12 04:01 PM arivero 3 2,175 I know that one of Goldbach's conjectures is that every even number is the sum of 2 primes. So, I was wondering if... Sep22-12 01:48 PM Norwegian 6 4,245 Hi all. I'm studying from Leon's Linear Algebra with Applications. I'm wondering if one of his examples has an error.... Sep18-12 11:37 PM chiro 4 1,392 I can easily visualize the 3 dimensional way to do so, and already have. I'd like to rotate from the... Sep19-12 12:24 AM chiro 2 1,029 Hi, I have a problem from a textbook on control systems along with the solution, but I'm not certain how the answer... Sep24-12 10:52 AM The Electrician 7 1,404 I am trying to prove that 11 is a prime in \mathbb{Z}. I noticed that \mathbb{Z} is not a UFD so I cannot show that... Sep17-12 11:42 AM mathwonk 2 1,100 I have a matrix A with real values that I wish to decompose into a proper orthogonal matrix R and a symmetric matrix... Sep17-12 01:15 AM Bavid 0 863 I'm trying to find if a number is odd or not, basically if X % 2 = 1. Can this be expressed through some function?... Sep25-12 08:48 AM Eval 13 2,167 Hi. I'm wondering if anyone can point me to any information on techniques to decompose a matrix (actually a 3D... Sep17-12 03:04 PM Stephen Tashi 6 1,880 Let $${x_1,x_2,...x_n}$$ be positive numbers. Consider the matrix C whose (i,j)-th entry is ... Sep17-12 10:21 AM dsantanu 0 802 Why are QR factorization useful and important? Sep18-12 11:05 AM hotvette 1 719 Hello, Scilab help states that If a matrix is badly scaled or nearly singular, a warning message will be... Sep23-12 11:46 AM sunny110 14 4,739 Say I have a mxn matrix A and a nxk matrix B. How do you prove that the matrix C = AB is full-rank, as well? Sep22-12 03:13 PM AlephZero 6 2,153 In 'Linear Algebra Done Right' by Sheldon Axler, a direct sum is defined the following way, We say that V is the... Sep19-12 02:02 PM omoplata 2 742 Am I right in saying that Zp x Zp (the product of the integers mod p, a prime, with itself) has only 3 nontrivial... Sep19-12 09:41 PM carrie.lugo 2 1,238 How can I prove that the set of all planar vector fields forms a vector space? Thanks for any input! Sep20-12 12:50 AM mathwonk 2 1,458 I have array of natural numbers from 1 to n. They are divided into m groups, where m*(m-1)=n. I need all m-1... Sep21-12 05:10 PM martika 2 1,595 I would like to find a 3D coordinate of a point (X) on a circle, knowing two points on the circle (P1,P2) which... Sep22-12 10:24 PM alaam2005 6 1,757 Suppose there is a set of complex variables \{x_i,\,i=1 \ldots M;\;\;y_k,\,k=1 \ldots N\} and a polynomial... Sep24-12 04:08 AM chiro 5 1,082 Does anyone know of a general approach towards the problem posted here: http://proteneer.com/blog/?p=1557 It... Sep21-12 05:02 PM exmachina 0 623 I'm reviewing Projective Geometry. This is an exercise in 2D homogeneous points and lines. It is not a homework... Sep22-12 05:40 PM Muphrid 5 1,219 Hello forum, why does a system of linear equations really have no solution or one unique solution, or infinite... Sep23-12 02:42 PM Studiot 7 1,145 I have to prove "For every integer n, n^2 is congruent to exactly one 0,2,or 4mod 7? I don't even know where to start?... Sep26-12 05:17 PM ramsey2879 17 2,784 Find two algebraic numbers (over Q) a and b each of degree 3 such that ab has degree 2. I have attempted to... Sep24-12 10:04 AM bessletama 0 580 Okay, so for the problem before this, I proved that L(S ∩ T ) ⊂ L(S ) ∩ L(T ). For this problem, I have to give... Sep23-12 09:42 PM TrapMuzik 1 624 Hi Can someone please clarify if you are trying to diagonalize a matrix and you find that one of your eigenvalue is... Sep24-12 04:58 PM HallsofIvy 4 959 Hi, A quick question: Does a set need to be a subset to be a subspace of some vector space? Sep24-12 09:22 AM Max.Planck 3 773 Prove that the polynomial $$x^{20}-2x^{13}+10x^{7}-6x^{2}-4x+100\in\mathbb{Z}$$ is irreducible or factors into... Sep24-12 09:57 AM bessletama 0 579 Find the general solution to the following system of equations and indicate which variables are free and which are... Sep24-12 09:03 PM Simon Bridge 1 842 u and v are contained in V Lets say the scalar multiplication is defined as: ex. ku=k^2 u or ku =... Sep26-12 10:29 AM Stephen Tashi 2 1,153 I'm required to diagonalize a 5x5 matrix by hand, using 'appropriate similarity transformations.' I'm not asking for... Sep26-12 05:02 PM Robert1986 12 1,917 Hello, I am reading a set of lecture notes on lattice QCD:... Sep26-12 09:58 AM evilcman 0 597 I have had absolutely no sleep for a while, so my math brain has been failing me. Last night, I was working on a... Sep28-12 10:03 AM ramsey2879 9 2,370 we know the equation above does not have integer solutions ( Fermat last theorem having been proven few years back ).... Sep27-12 07:24 AM epsi00 1 1,465 I am really confused about something. I know that if I have a vector space, then the dimension of that vector space... Sep27-12 10:09 PM dumbQuestion 5 883 The assignment is making use of the property of triangular matrices to find the inverse of a matrix \displaystyle A. ... Sep28-12 07:07 AM Ask4material 0 719