# Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
 Views: 92 Announcement: PF Member Award voting is open! Dec12-13 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 28,427 How important are linear transformations in linear algebra? In some texts linear transformations are introduced first... Sep28-12 07:40 PM Fredrik 4 1,087 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 11:52 AM The Electrician 7 1,097 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 09:48 AM Eval 13 1,773 Hello, Scilab help states that If a matrix is badly scaled or nearly singular, a warning message will be... Sep23-12 12:46 PM sunny110 14 3,495 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 11:24 PM alaam2005 6 1,240 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 05:08 AM chiro 5 951 Hello forum, why does a system of linear equations really have no solution or one unique solution, or infinite... Sep23-12 03:42 PM Studiot 7 818 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 06:17 PM ramsey2879 17 2,322 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 11:04 AM bessletama 0 505 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 10:42 PM TrapMuzik 1 559 Hi Can someone please clarify if you are trying to diagonalize a matrix and you find that one of your eigenvalue is... Sep24-12 05:58 PM HallsofIvy 4 724 Hi, A quick question: Does a set need to be a subset to be a subspace of some vector space? Sep24-12 10:22 AM Max.Planck 3 579 Prove that the polynomial $$x^{20}-2x^{13}+10x^{7}-6x^{2}-4x+100\in\mathbb{Z}$$ is irreducible or factors into... Sep24-12 10:57 AM bessletama 0 489 Find the general solution to the following system of equations and indicate which variables are free and which are... Sep24-12 10:03 PM Simon Bridge 1 747 u and v are contained in V Lets say the scalar multiplication is defined as: ex. ku=k^2 u or ku =... Sep26-12 11:29 AM Stephen Tashi 2 752 I'm required to diagonalize a 5x5 matrix by hand, using 'appropriate similarity transformations.' I'm not asking for... Sep26-12 06:02 PM Robert1986 12 1,385 Hello, I am reading a set of lecture notes on lattice QCD:... Sep26-12 10:58 AM evilcman 0 437 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 11:03 AM ramsey2879 9 1,798 we know the equation above does not have integer solutions ( Fermat last theorem having been proven few years back ).... Sep27-12 08:24 AM epsi00 1 1,218 x / y = z, so z * y = x 1 / 0 = x, so x * 0 = 1 But 0 does not equal 1, so x / 0 is unsolvable. Oh, and I'm new to... Sep29-12 09:22 AM ramsey2879 6 1,928 I am really confused about something. I know that if I have a vector space, then the dimension of that vector space... Sep27-12 11:09 PM dumbQuestion 5 723 When studying linear algebra when encountering a system Ax=b, I always read of the fundamental subspaces of A: N (the... Sep28-12 08:00 PM HallsofIvy 2 742 The assignment is making use of the property of triangular matrices to find the inverse of a matrix \displaystyle A. ... Sep28-12 08:07 AM Ask4material 0 583 I do not have access to the math calculators. Δ = 162*(a-b)*(a^2-b^2)*(a^3-b^3) -108*(a^3-b^3)*(a-b)^3 +... Sep28-12 11:12 PM epsi00 3 1,298 if M is dxd positive semi-definite matrix, then: M = L'(or L transpose) * L where L is a matrix of dimensions... Sep29-12 12:51 AM xponential 0 515 Hello, Let's have a group G and two subgroups A