Linear Algebra and Group Theory

Hi, I don't know if I post in the right section.. Infinity is a big part of mathematics. I've known for long time all the assertion in mathematics based on bijection : for instance the idea that the number of pair integer is equal to the number of integer because you can create the bijection n -> 2*n. This type of idea is mainly accepted as true, and used in different forms that conducts to strange ideas which are counter intuitive.. (the idea that infinity contains several different part of itself is counter intuitive). I've never believe in such ideas : and here's why I think we should reject the idea of bijection : To reason in infinite sets, we often …

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.

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 ><

Hi there everybody. Helping my brother to prepare for his Math Exam tomorrow and this problem really got me stumped. I could solve it with a tree, but that would take very very long and doesn't seen reasonable. Problem: Create a password that contains 6 characters. The first four characters must be a letter the alphabet, however the first and forth character must be a vowel. The last 2 characters must be a number (1 through 9). How many possible passwords are there. (no repetition of characters) Answer on memo is very confusing: 5*24*23*2*9*8

Hi I need to find g(t) here urgently conjugate{g(t-(tau/2))}* g(t+(tau/2)) = exp(pi*tau+iota*pi*t)

Hi, I had a little problem which I'd like to have answered! How to solve for x, given the following; 2Ln(x+4)+1=x ? the solutions are x= -3.91.. & 5.50.. Wolfram-alpha solves the problem using 'Lamberts W-function', which makes sense because using the inverse property of logs with exponents will not simplify this problem at all. But by using Using Lambert's Transcendental Equation, with the correct substitution of 'x' for another variable say 'u', I think it can be solved. Ln u = a u^b {b = 1} solution: u = exp [ -W(-a*b)/b ] , where W( ) is Lambert's W-function. Your thoughts? {http://mathworld.wolfram.com/LambertW-Function.h…

I'm not a mathematician, I'm a very close cousin, a physicist. I've been comparing the idea of a zero from the mathematicians' point of view and the physicists' point of view and find both somewhat incompatible. Maybe the term incompatible seem a little extreme, so allow me to use the term inconsistent. Here goes my argument; Mathematically, if you subtract 2 from 2 what would be left is nothing. This nothingness is what mathematicians call a zero. Physically, If you take away everything, from the largest of galaxies to the smallest of particles, eg gluons, photons, bosons, etc, what would be left? The philosopher would say nothing. The mathematician would say nothin…

Hi, I'm struggling with the following: I have a colored graph, and I used Bliss to find the generators group for the automorphisms. Finding the orbits given the generators is easy. What I'm trying to find now is dependence between orbits - for each orbit I want to know if it still exist if I"ll stabilize the rest of the graph, and if not, which of the other orbits need to be "free" to move with it. I tried searching in the computational group theory literature without success, but I may be missing some terminology here, any help will be appreciated. Thanks!

Is it possible to have a tensor, whereby one or more of its components are themselves vector? This relates to an earlier post.

Looking for an operation that converts a vector or tensor into a scalar, when the vector or tensor value is large. For example, if I multiply a row vector by a column vector, I get a scalar but I really need a function that turns a column vector into a scalar, when its value is significantly large, but if the vectors value is small, the function simply returns another vector. I would like it to work with tensors as well. I hope you find it an interesting problem - I am looking for a function, which can be an operation, but not another vector.

please tell me some apllications of lagrange's theorem in group theory... that are used in daily life...

I dont even know if there is an equation for this, but what is the equation for a quarter circle that has a center at the origin?

Help me to solve algebra 1 homework In a mixture of 60 liters, the ration of milk and water is 2 : 1. If this ratio is to be 1 : 2, then what is the quantity of water further added? Thanks

Hello, I'm working on a computer problem, but, before I waste too much time going down this road, I thought I should pick the brains of you math geniuses. Basically, I want to be able to represent any number between 1 billion and 42 trillion using just 4 characters (numbers and/or letters). This is what I've come up with so far... A^a + B^b + C^c + D^d = LARGE NUMBER a, b, c, & d are exponent variables that can range from 0 to 35 (0,1,2,...X,Y,Z) A, B, C, & D are bases that are integer constants that never change. Basically, if someone is given the 4 exponent values and the bases are already known, they can extrapolate the number value …

I'm trying to use the vibrational frequency equation to calculate the frequency constant, but i can't seem to rearrange it correctly! Here is the method i used: v = 1/2π x √kf / m therefore: v/1/2π = √kf / m (v/1/2π)2 = kf / m (v/1/2π)2 x m = kf Can someone please pick a hole in my rearranging, because i know the actual rearranged equation and this is not it!

1) Primitive symbols: (*,1) 2) The axioms: a) for all x,y [x*=y* => x=y] b) for all ,x [ x* is not equal to one] c) 3) Prove: for all ,x :if x is not equal to one ,then there exists a unique y such that y*=x

This thread attempts to address (albeit in a somewhat oblique way) some issues in elementary set theory that have emerged here. I promise you will enjoy it, but first let me freely confess I have posted this elsewhere. I dare say it is against the "rules", but then...... Before the fun starts, we have to do a bit of homework. The cardinality of a set is simply its number of elements. If [math]S[/math] is a set, then its powerset [math]\mathcal{P}(S)[/math] is simply the set formed from all its subsets. Thus, bearing in mind that [math]S, \,\,\, \O[/math] are always subsets of [math]S[/math] ([math]\O[/math] is the empty set, btw) then, when [math]S=\{a,b,c\}[/…

Is this the correct folder in which to pose a question on differential topology? To help keep things simple, suppose you have a 2-form on a manifold of dimension 2, having metric type (+, +), rather than an arbitrary number of dimensions and other metrics. As I understand it, we can integrate a k-form over an n dimensional manifold where k=n. But I want to do an incomplete integration: Given, L an antisemmetric tensor, [math]L=L_{[ij]} dx dy [/math] define [math]S = \int L = \int L_{ij}dx dy[/math]. However, I would like to partially integrate L. [math]S_y dy = ( \int L_{ij}dx ) dy[/math] and …

hello . can anyone recomment me a free software for create subset from a set ? thanks

Where to see proof of the fact that the linear space is left free module over the ring?

Im having some trouble finding exact practical relations to other things such as practical uses in chaos theory or astro physics in general. Can anyone tell me how linear algebra is used in chaos theory or other astro sciences?

I am ashamed to ask this, but here goes..... We know that if a vector space is finite-dimensional, then there exist subsets of finite cardinality that will seve as a basis for this space iff all elements of these sets are linearly independent. We also know that this implies that any subset containing the zero vector cannot be a set of linearly independent vectors, and is therefore not a suitable basis for our space. I now find that, in the case my vector space is not finite-dimensional, then the basis set may contain "only finitetly many non-zero elements". On the assumption that a non-finite vector space has a basis set of non-finite cardinality, then it…

Hello, I have problem with finding every possible number value of [latex]GCD(a^2b+b^2c+c^2a, ab^2+bc^2+ca^2, a+b+c)[/latex] where assumptions are: [latex]a,b,c[/latex] are three different integer number, [latex]GCD(a, b, c)=1[/latex] and [latex]a,b,c > 1[/latex]. I tried first find the [latex]GCD(a^2b+b^2c+c^2a, ab^2+bc^2+ca^2)[/latex] and next [latex] GCD(GCD(a^2b+b^2c+c^2a, ab^2+bc^2+ca^2), a+b+c)[/latex] by euclidean algorithm but it wasn't work for me, also i don't know how to use the assumption [latex]GCD(a, b, c)=1[/latex] I checked a couple examples in wolframalpha and it always return 1 so I guess it is the answer but I can't prove it.

I am not a mathematician, but rather a musician who met a problem (it's not homework!) that can possibly be posed as a mathematical problem. So I'm looking for a solution but also and especially for a direction to the discipline that may solve the problem. I apologize for bad use of proper mathematical writing. Let's say I have the whole set of all 64 possible 6-tuplets of digital bits, such as 000000, 000001, (000010) and so on up to 111111. Of course I can operate on couples of 6-uplets in order to have the XOR result. For example: 010101 XOR 11000 = 011010. I would like to put the 64 6-uplets in such an order (a cyclic one with period 64, that is to say in circle…

I'm sorry this is a stupid question. Obviously if ag = bg then ag(g inverse) = bg(g inverse) => a = b I shouldn't post questions late at night. In the definitionof a group action say of a group G on a set S, there are two conditions: 1 for a in S and e in G where e is the identity, ae = a. 2 for a in S and g and h in G, (ag)h = a(gh) Where does it say that if a and b in S and g in G, that ag is not equal to bg? They always say that for ag = z then obiously there is an inverse g- that zg- = a. One could add another condition but nobody ever does. Thanks