Linear Algebra and Group Theory

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

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

Dear all, I have a query regarding the Sylvester's Law of Inertia (Congruence Transformation). It says the following (taken from Gilbert Strang---- 4th edition, Page 324) : C^T*A*C has the same number of positive, negative and zero eigenvalues as A, for some nonsingular matrix C. That is, the signs of eigenvalues are preserved by the congruence transformation. Here, I give 2 matrices A and C^T*A*C where the signs of the eigenvalues do not seem to be preserved: A = -10.0000 -0.2000 -0.1500 5.0000 0.1440 0.3600 5.0000 -2.0000 0 -2.5000 1.4400 0 0 1.0000 -3.0000 0 -0.7200 …

Hey I was toying around with an idea that vaguely resembles vertex-edge graphs. We have two locations: A and B. The objective is to get from A to B going from point to point in the region in between. One is not allowed to go back to a point already taken. It was a simple observation that given [math]n[/math] path points, there exist [math]n+n(n-1)+n(n-1)(n-2)+...+n![/math] possible unique pathways one can take. For example, with 4 path points in between, (labelled m, n, p, q), one can take [math]4+4(3)+4(3)(2)+4(3)(2)(1)=64[/math] pathways. The number of terms in the above general formula changes according to how large [math]n[/math] is. So question: Is t…

Hi. I got a problem which is related to Probabilities Theory. Suppose that we have a system that consists of, for example, 5 parts a, b, c, d and e. And also we have these informations: If a fails, the system will fail with probability of 50%. If b fails, the system will fail with probability of 40%. And If c, d and e don't fail, the system won't fail with probability of 35%, 40% and 45% respectively. Now this is the question: What is the probability of the system not being failed, if a and b are failed and c, d, e, aren't. Please explain the method, too. Thank you for your help.

Given that f(x) = 2x^2 + x - 5 and g(x) = x + 7 Find the compositions f o g and g o f and determine the domain of fog.

There is allegedly a theorem related to spaces that states, in effect, that an object within a space of n dimensions cannot move unless it exists within a space of n+1 dimenstions. Example: Imagine a genuinely 2-dimensional sheet of paper resting atop a 2-D surface. The paper cannot be curled or folded unless it exists within a 3-D space. Does anyone know of this theorem? Even better, can anyone prove it? It is relevant because if it is true, movements of 3-D objects within a 3-D space would not be possible unless they exist within a 4-D space. (In this context time does not count as a dimension.) IOW if this theorem exists and its proof is mathemati…

I should point out that the term "set capacity" is totally made up and informal. As always, you can alter and/or repost my images, and you don't need to give credit because they aren't copyrighted. I learned about Venn diagrams recently. When I attempted to make a 4-set diagram, I realized that the classic intersecting circle approach didn't cut it. Where A and C are opposite circles in the diagram below, A and C don't have an intersecting region that doesn't also intersect B or D. According to Wikipedia, this is actually a Euler diagram. http://en.wikipedia.org/wiki/Venn_diagram#Extensions_to_higher_numbers_of_sets Wikipedia gives some alternatives f…

Hi Everyone, I want to know the kurtosis of salt and pepper noise. It's a noise which are added on the extreme values of an image due to saturation. A paper says that it's always greater than 20, but according to my observations, it's greater then 20 when percentage of noise is less than 10. For higher percentages, it's smaller.http://www.andor.com/learning-academy/read-noise-understanding-scmos-read-noise see the link for a histogram of impulse noise.

Can someone suggest an algorithm to solve job assignment problem with condition? With condition means that some jobs cannot be done by some workers. For example table as shown below: In this table x - means that it is impossible to do. For example, worker 1 cannot do jobs 1,3 and 5. I encountered such situation and there may be cases as shown above when usual Hungarian algorithm seems cannot solve such task because there is no way to complete all tasks by distributing one task per worker. However, my main case it is allowed that one worker wil do several tasks (tasks, which worker can do). Main task is to complete all jobs using existing workers, but it is …

We had our first test and I'm trying to understand what it is I'm missing. I list each of the questions below, followed by what I answered. 1. Let v1=[ 1 ] and v2 = [ 1 ] --- Find a nonzero vector w that exists in R^3 such that {v1, v2, w} is linearly independent. [ 1 ] [ 2 ] [ 1 ] [ 3 ] ans: w = [ 1 ] this was assuming that as long as the vector was a multiple of the of the vectors then the set would be linearly independent. [ 4 ] [ 6 ] 2. Find the general solution to the equation A*x = 0 (where x is a vector). Give your answer in parametric vector form. A = [ 1 2 0 -2 0 ] [ …

This problem origins from Mathematics for Engineer and Scientists 2nd ed - Alan Jeffrey P670 Chapter15.6 System of first order equations [latex]\displaystyle \dot{y}+2\begin{pmatrix} -3 & -2 \\ 5 & 3 \end{pmatrix} y = 5\begin{pmatrix} 1 & -1 \\ -1 & 2 \end{pmatrix} \begin{pmatrix} e^t \\ e^{-t} \end{pmatrix} [/latex] Try particular solution [latex]\displaystyle y_p=X\begin{pmatrix} e^t \\ e^{-t} \end{pmatrix}[/latex] [latex]\displaystyle \dot{y_p}=X\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \begin{pmatrix}e^t \\ e^{-t}\end{pmatrix}[/latex] substitute [latex]\displaystyle \dot{y_p}[/latex] and [latex]\displaystyle …

Hi, I have found an encryption algorithm named ECKS-PS (published in a paper named 'efficient conjunctive keyword search on encrypted data storage system', written by Jin Wook Byun, Dong Hoon Lee, and Jong In Lim) that allows an user to search in encrypted data. The algorithm is described here: http://img210.imageshack.us/img210/4644/eckps.png (I have written out the steps a little bit more clear here: img801.imageshack.us/img801/3373/stepsecksps.jpg) I have tried multiple times to use the algorithm to search for an encrypted word, but I never get a match between the left part of the equation and the right part of the equation. (see calculations: http://img4.im…

Hi guys, I am struggling with finding eigenvectors of a 3x3 matrix in a change of coordinates problem. Basically, I have taken the equation x^2 - z^2 - 4xy +4yz, converted it into matrix [1 -2 0; -2 0 2; 0 2 1] and found the eigenvalues 1 1/2 + sqrt(33)/2 1/2 - sqrt(33)/2 But I am truly struggling with the eigenvectors here. The first one (l=1) is easy, but the other ones not. I plug the eigenvalues in the matrix and using Gauss-Jordan, I only get 1's on the diagonal. But I cannot determine such a vector, as I would think that it is [x1 x2 x3] = [0 0 0]. Help?

I don't know a lot about number theory and I haven't taken any math classes higher than Calc 1, but I have been playing around with a question: How many exponents of 2 lie between each exponent of 10? i.e. 2, 4, 8 (3) 16, 32, 64 (3) 128, 256, 512 (3) 1024, 2048, 4096, 8192 (4) ... I did this using Ruby and got up to 20,000 decimal places (I don't own a supercomputer) and averaged the results of each exponent of 10. The result I got was an average of 3.322 exponents of 2 between each exponent of 10. I would like to know if this is a well-known problem and what this average is as the decimal places approaches infinity. I would also like to know if there…

I'm reading a paper currently that uses three groups; the cyclic groups of order 3, 5, and 11. It represents an element from C3 as (c, 0, 0) an element from C5 as (0, c, 0) and an element from C11 as (0, 0, c). What is the motivation for representing the elements like this? i can understand that it is easier for calculations but if someone asked me why you can represent each element as a vector i would not be able to explain why you are allowed to that.

can anyone help me to diagnolize this matrix? |L M M| |M L M|=A |M M L| we should use eigen values and eigen vectors when we have numbers it's so easy we find them and then the diagnolized matrix is equal to = eigenvectors matrix*inverse of eigenvecros matrix*matix A but when we have parameters i think its diff PLEASE HELP ME

I want a matrix W of size nxk (where n>>k) with the following two properties: 1. Sum of all elements of each row is equal to one, i.e. Sumj wij = 1 for all i. 2. Sum of squares of all elements of each column is equal to one, i.e. Sumi wij2 = 1 for all j. Is such a matrix possible? Any hint at how to prove one way or the other would be appreciated. Thanks in advance.

Hi there, you may remember me from various computer science, climate science, and politics threads. Well I'm back! With a question about cryptography. But really this is a question about group theory/finite fields/abstract algebra (I think). I really have no formal understanding of any of that, but I have been trying to wing it so far, and this is what I've come up with: a failing system. I am trying to build a "semiprivate key system" using the Networking and Cryptography Library and more specifically Curve25519, which is a form of twisted Edwards curve. It looks like this, as formally as I can describe it: https://gist.github.com/tarcieri/4760215 And…

Dear, does anybody has some idea how to solve this system of equations> X*A+B*X'-C=0. A=[2674.015 1007.506 -979.980 673.29 -1332.007 7.506;-5.317 -1.969 1.750 -1.291 2.777 -1.969;-2808.466 -1058.120 1028.797 -707.075 1399.196 -1058.120;-5363.677 -2020.687 1964.589 -1350.219 2672.592 -2020.687;5382.325 2027.684 -1971.321 1354.875 -2681.975 2027.684;-9.889 -3.691 3.424 -2.442 5.055 -3.692] B=[-1.679 -1.266 -120.123 -0.166 -0.686 -1.266;-0.525 -0.432 -43.874 -0.0375 -0.303 -0.432;4.714 4.857 685.238 -0.057 5.058 4.857;-0.274 -0.255 -28.164 -0.0077 -0.230 -0.255;1.229 0.805 66.092 0.171 0.208 0.805;-0.525 -0.432 -43.874 -0.037 -0.303 -0.432] C=[9.931 3.696 -12.77…

WHEN I ENTER ANY NUMBER GREATER THAN 1 IN A CALCULATOR AND KEEP SQUARE ROOTING THE SQUARE ROOT OF THE NUMBER, I WILL OBTAIN 1. ALSO IF THE SAME IS APPLIED TO ANY NUMBER GREATER THAN 0 BUT LESS THAN 1, THE RESULT IS 0.999999............. TO INFINITY. WT IS THE CAUSE AND IMPLICATION OF THESE RESULTS. PLEASE TELL ME AS SOON AS U CAN

Let G be a finite group. A group G is simple if the only normal subgroups of G are the identity and . What does mean for a group G to be nonabelian simple group? What does mean for a group G to be not nonabelian simple group?

http://www.youtube.com/watch?feature=player_embedded&v=uXOTKidm7A0 base 1?

Hi I want to solve 3 or 4 or up to n degree equation I tried many time to solve only 3 degree equation but cannot solve ax3+bx2+cx+d=0 x=? a0xn+a1xn-1+a2xn-2+....+an-1x+an=0 what is general formula to calculate value of x? I'm not talking about calculus which can give value of x by Newton's method I want algebraic solution!