# 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: 82,459 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 34,085 Hi, I have a rather trivial question but google did not really help me. So far I was always familiar with the fact... T 07:27 AM HallsofIvy 2 55 I heard about fast tridiagonal matrix algorithm. I tried to find what is it but I can only find tridiagonal matrix... Y 11:58 AM Shyan 0 68 Just one simple doubt here. Can we use different scales on the x and y axes be used for denoting linear... Jul22-14 06:48 AM HallsofIvy 2 270 I know it should be absolute zero, but in a scientific calculator, which is an app actually, its value is shown... Jul21-14 05:34 AM Adit 3 160 Hello, I am going over these slides and I am very confused on a couple parts. First of all on the first slide, I... Jul20-14 01:19 PM WWGD 6 227 Hello everyone! I've been learning some basic group theory (I'm new to the subject). And I had a (hopefully) fairly... Jul19-14 06:37 PM WWGD 3 236 Hi,let: 0->A-> B -> 0 ; A,B Z-modules, be a short exact sequence. It follows A is isomorphic with B. . We... Jul19-14 03:16 PM WWGD 4 834 Problem 1: Use Gaussian elimination with back substitution to solve the following system. Problem 2: Use the... Jul19-14 12:38 PM micromass 6 438 Hi, Given several vectors, which may be or not be orthogonal to each other, how to construct a vector perpendicular... Jul18-14 06:25 PM WWGD 4 309 I am working with polytopes that are defined by half-planes in \Re^N. So they are defined by a number of inequalities... Jul18-14 04:11 PM sloppyintuit 2 299 Hi All, Let A,B be algebraic structures and let h A-->B be a bijective homomorphism. Is h an isomorphism? In... Jul18-14 12:01 PM WWGD 2 409 Use Gaussian elimination with back substitution to solve the following system: x1+x2+x3=1, x1+2x2+2x3=1,... Jul17-14 09:34 PM Math10 3 498 Hello, Been a long time lurker, but first time poster. I hope I can be very thorough and descriptive. So, I have... Jul16-14 04:02 AM nikphd 4 842 Hi all, Suppose I have a matrix A_{N\times N}. I compute its eigenmodes A V = V \Lambda. V, \Lambda are... Jul15-14 08:06 PM AlephZero 1 638 The killing form on a lie algebra is defined as $$B(X,Y) = \text{Tr}ad_X \circ ad_Y$$ where ##ad_X: \mathfrak{g} \to... Jul14-14 05:44 PM Terandol 1 881 Hello, Given the complex linear mapping: T(z) = Az + B where A is real and B is complex. However trying to show... Jul14-14 03:57 PM WWGD 3 671 The definition (taken from Robert Gilmore's: Lie groups, Lie algebras, and some of their applications): We have... Jul14-14 01:22 PM Travis091 6 836 Two groups are isomorphic if they has same number of elements and if they has same number of elements of same order?... Jul5-14 05:24 PM NeoAkaTheOne 12 4,370 Can you guys give me a concrete example of a completely positive map from M_m → M_n? Jul3-14 06:26 PM WWGD 2 1,721 Hi, i was wondering how the following expression can be decomposed: Let A=BC, where B, C are rectangular random... Jul2-14 04:54 PM MisterX 2 1,808 I am trying to diagonalize the following matrix: M = \left( \begin{array}{cccc} 0 & 0 & 0 & a \\ 0 & 0 & -a &... Jul2-14 12:45 PM Trifis 2 1,377 I need help solving for t in the following equation, |P + Vt + A(t^2)/2| = st where P V and A are vectors and s... Jun30-14 04:45 PM jedishrfu 3 1,520 I've been reading about algebraic geometry lately. I see that a lot of authors use ##V^\vee## to denote the dual space... Jun29-14 10:45 AM Mandelbroth 2 1,947 Hi. In this development (c ∇+ d A)(c ∇+dA)= c^{2} ∇^{2} + d^{2}A^{2} + cd A∇ + cd ∇A (c ∇+ d A)^{2}= c^{2} ∇^{2}... Jun28-14 11:49 AM Fredrik 9 1,457 Hi, Can someone explain me the division operation in the picture. First for left division we use (.\ ) not only ( \ )... Jun26-14 06:22 PM HallsofIvy 4 1,447 I was reading in my textbook that the scalar product of two complex vectors is also complex (I assuming this is true... Jun23-14 08:16 AM Fredrik 4 1,360 Hello, first of all, sorry if my question is either trivial or imprecise, I'm from the engineering domain :) I... Jun23-14 06:26 AM Erland 1 1,349 Hey, So I am trying to do a tri-quadratic curve fit (linear regression) in excel. I have successfully completed a... Jun20-14 11:37 AM mattskie 2 1,391 1. Is there a general condition for the existence and uniqueness of solution of a system of simultaneous non-linear... Jun19-14 07:40 AM Chestermiller 7 1,556 Please excuse my terminology as I am teaching myself linear algebra. I am attempting to construct a vector which... Jun18-14 08:52 PM Simon Bridge 14 2,165 I'm interested in spherical geometry in 4 dimensions. Surely someone has done this, but what is it called? I can't... Jun17-14 03:08 PM micromass 1 1,298 I've been reading Kreyszig's functional analysis book, and I'm a little confused why he defines the spectral family of... Jun17-14 02:29 PM micromass 1 1,273 Hello guys, Let ##T: \mathbb{R^2} \to \mathbb{R^2}##. Suppose I have standard basis ##B = \{u_1, u_2\}## and... Jun17-14 06:08 AM Seydlitz 4 1,419 I want find a value M such that given v and u, satisfies the equation v=Mu. Well, the vector u has a modulus u and... Jun15-14 06:40 PM WWGD 11 1,481 Hi. This is driving me mad: \hat{\vec{\nabla}}(\hat{\vec{A}})f=(\vec{\nabla}\cdot\vec{A})f +... Jun15-14 02:00 PM carllacan 4 1,383 In a previous thread, I asked a question different from that I actually intended to ask. Since this question is licit... Jun15-14 12:58 AM micromass 4 1,351 Hello, Thanks to the help of micromass in a previous thread, I am now able to prove the following theorem (which... Jun14-14 05:36 PM coquelicot 5 1,365 My Goal: to find what fraction of my monthly payment should go to each loan. The ideal outcome would be to pay the... Jun14-14 12:19 AM Stephen Tashi 4 1,422 The gist of the approach I took is that∑1/p = log(e^∑1/p) = log(∏e^1/p) and logx→ ∞ as x→∞. Proof outline: let ∑1/p... Jun13-14 06:43 PM mathwonk 5 1,428 Let R be an integral ring (eventually can be supposed integrally closed), and R' an integral extension of R. Assume... Jun13-14 06:40 PM mathwonk 4 1,385

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