Linear Algebra and Group Theory

hey frnds...plzz help me in finding applications of group theory used in real life.....plzz help me....

I am fixing to start college and I need the best allround scientific calculator. I will probably be doing a little Algebra Geometry and Trig. What would ya suggest?

Hello! I was wondering if someone can help with how Trace(AB) can be equal to Trace(BA)? Thanks!

In case anyone here hasn't noticed, there have been a lot of debates on this online between people on other forums, some with a good grasp of mathematics and some without. The debate is over whether 0.999 does or does not equal 1. There are many different proofs to prove that it does, but because some people understand some proofs better than others, and some not at all the debates still go on. I've personally been involved in these sort of debates and I can think up at least five different proofs, all based on different sorts of logic, that show that they are equal. The more forms we can find, the better the chances are that someone will understand it. I thought …

I have found X=((I-A)^-1)(B), but in my book it says X=((I-A)^-1)(-B). Can't. figure out... Any one? Also I don't know if there is any matrix equation solver like this on the internet I have searched but it's not exactly what I want.. Thanks, exam tomorrow ><

I need the help of a math's wizard, because I am confused by something.... The odds of winning £10 on the Lotto are 56.7 to 1. Ok. But I have been told that if you write 57 lines of numbers, no matter what they are, you can't always win £10. In fact I have been told that you need 168 lines of numbers to guaranty £10. Could anyone explain the mathematics behind this in simple terms please. I am trying to write a computer program to find the smallest number of lines possible. I also want someone to be able to type 6 numbers into the computer, and the computer will make the smallest number of lines using those numbers. Pincho

This should be laughably easy, but I am a little confused here. Suppose that the function [math]f: \mathbb{C} \to \mathbb{C}[/math]. Suppose further that [math]z \in \mathbb{C} = x +iy,\,\, x,\, y \in \mathbb{R}[/math]. What is meant by the complex conjugate of this function? My thoughts (such as they are!). Set [math]z = x +iy[/math], and set [math]f(z) = ax+iby[/math] and [math]\overline{f(z)}= ax-iby[/math] Apparently this can be written as the identity [math]\overline{f}(z) = \overline{f(z)}= ax-iby[/math], which I don't quite get. Moreover,...... ...... how does this differ from, say, [math] f(\overline{z}) =\overline{ax+iby}[/math]?

For matrices, if AB=I, then does that mean BA=I also? If I have 2 matrices and I have AB=I, is that sufficient to conclude that B is the inverse of A? Or do I have to calculate BA explicitly too? I've tried finding a simple 2x2 counterexample but I can't find any. All examples of AB which I've conjured up also have BA=I.

Ann and Bill independently work on examples of Cantor's diagonal argument. Ann: 111001... 000111... 101100... 110011... 000110... 010110... transforms diagonal D1 to alternating '01' sequence T1, 010101... which can't appear in any list per the cda. Bill: 000110... 010110... 110001... 000111... 101100... 110011... transforms diagonal D2 to alternating '10' sequence T2, 101010... which can't appear in any list per the cda. If D1 and D2 appear in any list, they must be members of the complete list. T1=D2. I.e. a missing sequence is only relative to an individua…

what's the proof for the discriminant [math]b^2-4ac[/math]? e.g. Proove that if [math]b^2 > 4ac[/math] then x has 2 real and distinct roots.

In terms of the reference frame used in geometrical modeling, is there a difference between "Euclidian Geometry" and "Cartesean Coordinate Systems"? One thing I'm wondering is, how is Euclidian Geometry possible without a Cartesean Coordinate System? Yet, Descartes is credited with inventing the Cartesean system 2 millenium after Euclid invented his geometrical system. The Cartesean system cannot have been new in the 17th century - maybe given a new name, but not new.

When defining the dot product, the cosine of the angle between two vectors is chosen. Why not the sine? What advantages are there by choosing the cosine?

This is a question that doesn't have a solid question... Now we use math in everything we do... even on my laptop that I am using for this thread uses mathematics to solve and put in every single pixel on screen... We count words and letters in our language books and count the thousand habitable planets in our solar system. We draw graphs and charts for buisness and the economy needs to know how much they have of anything. But first the big picture. To define everything is like to define 'god'. It is impossble, because we all have a different oppinion or definiton of that. Science has something to do with math. We can't count the amount of atoms that exist in and …

After talking with Rev, it became apparent, that I need to review linear transformations. Last night, I spent about 4 hours reading through 3 different books on linear algebra. All I want to do right now, is fully and competently understand what a linear transformation is. Here is where I am at, and would appreciate any help. Ok first of all... The first thing that became apparent to me, was that I need to be able to logically express the concept of "exactly one," as opposed to merely "there is at least one." And I am a stickler about my logic. So for right now, I would like know exactly how some of you address the issue of "exactly one" using symbol…

I found the eigenvalues of a 2x2 matrix with all elements equal to one to be 2 and 0. The eigenvalues of a 3x3 matrix with all elements equal to one to be 3,0,0. A 4x4 matrix to be 4,0,0,0 I stopped at a 5x5 matrix. I was just wondering (as i'm rubbish generalising things) whether this results holds for any size matrix. Also, are there any links were this is explored, i couldn't find any.

Is it just me, or is this whole imaginary number stuff just a bunch of crap? I learned this in Algebra II class the other week. Now, my teacher is trying to apply it. What meaning will this have in my life? Don't get me wrong, I understand the concept...but, why do I need to know this?

Hi everyone! This seemingly easy question is proving difficult. I have to show that a field automorphism of R to R (real numbers) is the identity. What I've done: Let f:R -> R be an field automorphism. Since f(1)=1 is a generator of Z, f is the identity on Z. Because multiplicative inverses are sent to their inverses: f(1/x)=1/f(x), it follows that f is also the identity on Q. I`m not even sure if I`m on the right track. I obviously have to use some property of the reals now. A previous exercise which I very likely need to use asks to show that if x>0 then f(x)>0. Any help is appreciated.

What is SO(3)?

I tell non-math I'm studying linear algebra and they say: "that sounds like something I took in sixth grade." So why call it linear algebra? It is supposed to be in contrast to "abstract algebra" ? Thanks

Question: Show that S4 has a unique subgroup of order 12. So far I know that A4 is a subgroup of order 12. So I was trying to prove by contradiction that there was another subgroup of order 12, say G. So the (|G||A4|/the intersection of G and A4) = 24. Then I need to show something to the effect that the intersection of G and A4 has to be a subgroup of order 6 in A4 and that that is a contradiction. This is as far as I got and my teacher says I am on the right track, but I have no ideas of where to go next, help please!

I understand that Minkowski (Poincare?) Space is a Group in Group Theory.(am I right so far?) Well I have (re) learned that for a Group to be a Group there are one or two (4 ?) basic preconditions and that these are (1) that the set must have a operator and (2) must also include an identity element , (3) be commutative in the operations and that (4) each element must have an inverse. Oh and (5) it must exhibit "closure" How do these conditions apply to Minkowski Space? Are the elements of the set spacetime vectors? Are all the vectors unit lengths or can they be any length? What is the operation ? Is the set infinite? Have I got the…

Can somebody post (or direct me to) a proof/explanation that an outer product always has rank 1? Thanks!

I never understood this concept. What proof backs this up? This argument is sometimes also presented as "2 + 2 = 5 for large values of two." This doesn't make sense to me whatsoever. Can someone please help?

I need help on this question : The sum of three times a number and 11 is 32. Find the other number..

Can someone tell me what the origin of zerois???