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Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
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Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
1 30,465
Can matrix representations of clifford algebras of type Cl(0,n) be found? Specifically for even orders
May2-11 08:21 PM
2 1,264
One way to think about the seive of Eratosthenes is to imagine that after each pass, the non-deleted numbers are...
May2-11 02:45 PM
2 1,039
Hello, is there a straightforward way, or some well-known expression to count how many ways there are of choosing N...
May6-11 03:06 PM
2 5,072
Concerning Hardy-Littlewood approximate functional equation for the \zeta function \zeta(s) = \sum_{n\leq...
May8-11 08:41 AM
2 1,592
Ok this question is in a cd quiz from a text book, i have no idea what the question even means or how to do it. Please...
May9-11 08:42 AM
2 1,446
sorry im new and posted instead of currently writing the post
May16-11 09:26 AM
2 1,614
Gday, I was wondering if someone could tell what the nullity of an nxn zero matrix is? I can't decide if its zero...
May14-11 11:19 PM
2 2,335
Hello, I'm having difficulty understanding how to solve the following question using Sylow's Theorem: Suppose G...
May15-11 03:54 PM
2 1,583
Can someone recommend me a 2nd year linear algebra textbook that is good for self-learning? The course is linear...
May15-11 05:14 PM
2 1,523
Given a linear tansformation T of a vector space V (over a field K) with eigenbasis {v_{1},....,v_{n}}, and a...
May16-11 10:45 AM
2 1,642
I have a general sort of structural question. I have been reading a lot of maths papers lately, and it seems there...
May20-11 05:41 PM
2 1,082
Hey Im having trouble of how to go about this. Afterwards we have to perform some Cramers rule operations however...
May21-11 09:32 AM
2 1,595
Hello everyone, I'm new to PF, so I hope this post is in the correct location. Anyway, does anyone know why one...
May22-11 11:28 AM
2 1,557
Hi folks, If I have a Lie algebra \mathfrak{g} with an invariant (under the adjoint action ad of the Lie algebra)...
Jun14-11 11:50 AM
2 1,301
T is a linear operator from the space of 2 by 2 matrices over the complex plane to the complex plane, that is T:...
May31-11 12:16 PM
2 3,355
It's my understanding that algebraic numbers are the roots of polynomials with rational (or equivalently integer)...
May30-11 08:35 PM
2 1,671
Hello, I have a row vector defined as, X=\{x_1,x_2,\ldots,x_L\} I wish to "stack" this vector vertically, a...
Jun3-11 10:07 PM
2 1,653
I'm having trouble showing that any normal linear transformation T is the sum of a self-adjoint transformation T1 and...
Jun5-11 03:54 PM
2 1,864
Greetings. This is my first post, please be gentle! I am a music theorist who uses a lot of math in my...
Jun6-11 07:33 PM
2 1,485
I have two systems of linear differential equations: \frac{dx}{dt}=Ax, \frac{dy}{dt}=By x,y are vectors of length n...
Jun10-11 06:00 PM
2 742
* I have already posted this in the General Math, but I guess the problem is more like a linear algebra problem. ...
Jun9-11 04:41 AM
2 981
Arg\xi (1/2+iz) however i am a bit ashamed because the Riemann Xi function is real for real 'z' so for ALL the...
Jun11-11 04:35 PM
2 1,676
Hi, Algebraists: Say I'm given a group's presentation G=<X|R>, with X a finite set of generators, R the set of...
Jun18-11 07:13 PM
2 1,054
polynomial? i find this but i do not understand;its too complex. ...
Jun11-11 07:16 AM
2 2,185
Hi, I have this problem, 1) Find 1 + 2 + + n by summing the identity (m + 1)2 − m2 = 2m + 1 from m = 1 to...
Jun12-11 10:31 PM
2 1,764
Suppose that the set of functions \{P^a:\mathcal S\rightarrow \mathcal L|\,a\in \mathcal L\} has the property that for...
Jun11-11 07:26 PM
2 621
For two matrices A and B, when p(A)=0 iff p(B)=0 for any polynomial, what will happen? i read that A and B have the...
Jun13-11 02:13 PM
2 1,194
Hello all :) I am studying divisibilities of 1, 11, 111, 1111, 11111 and so on when I have even number of 1s, in...
Jun13-11 08:46 PM
2 1,499
I have a non-homogeneous Ax=b (with b non-zero) and i want to know if the set of all the solution vectors, x, forms a...
Jun14-11 04:03 AM
2 2,161
I came across this question. How do you show that √N is irrational when N is a nonsquare integer? Cheers.
Jun16-11 07:12 AM
2 2,169
I have a question I need to resolve before my exam on thursday. It relates to the following result: Let N be a...
Jun14-11 01:25 PM
2 948
The prime number theorem describes the distribution of the prime numbers, in a sense. Are there other prime number...
Jun15-11 08:12 PM
2 1,708
I'm wondering why 1/k! is needed in Alt(T), which is defined as: \frac{1}{k!}\sum_{\sigma \in S_k} \mbox{sgn}\sigma...
Jun18-11 10:13 PM
2 1,135
Is saying \existsx, \existsy the same as saying \existsy, \existsx?
Jun17-11 10:54 PM
2 1,614
i have ordered introduction to linear algebra by gilbert strang.But i saw it on google books and found it to be...
Jun18-11 09:53 PM
2 2,388
Sorry if this is a well known thing, but I've noticed this and decided to see how well known it is, also if there is a...
Jun19-11 10:14 PM
2 2,552
Hi, All: Could someone please tell me or give me a ref. on the basic properties of Gl(n,R) ; R a ring;...
Jun20-11 08:34 PM
2 1,436
So Sylow's second theorem tells us that if G is a group, p a prime, and H,K are both p-Sylow subgroups, then \exists...
Jun22-11 11:36 AM
2 1,248
I don't understand how order 1 alternating tensors fit the definition of alternating tensors. I think the order has to...
Jun23-11 04:20 PM
2 1,294
I wanted to make clear just a quick technical thing. If G is a group, N is a normal subgroup, and \phi_g \in...
Jun24-11 01:30 PM
2 1,319

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