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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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Jan16-12 Greg Bernhardt
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 33,963
A lattice is a partially ordered set such that every finite set has a least upper bound and a greatest lower bound....
Jun26-11 09:26 AM
Fredrik
3 1,199
I'm curious why people develop these objects. Although I've seen some proofs of theorems using coset(or quotient space...
Jun26-11 01:04 AM
kof9595995
6 2,033
According to duality principle, a bilinear function \theta:V\times V \rightarrow R is equivalent to a linear mapping...
Jun25-11 07:42 AM
micromass
3 1,718
Hey there I would just like some help in rearranging the formula: z=\frac{1+\frac{v\cos...
Jun24-11 02:52 PM
Pretty Pony
2 1,460
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
Kreizhn
2 1,408
The matrix giving the relation between spherical (unit) vectors and cartesian (unit) vectors can be expressed as: ...
Jun24-11 05:29 AM
nceba
4 1,479
http://www.math.northwestern.edu/~clark/285/2006-07/handouts/lin-constraint.pdf It's actually proof of finding...
Jun23-11 09:37 PM
holemole
1 1,675
I know that the nth Fibonacci number is defined as: \frac{{1+\sqrt{5}}^{n}-{1-\sqrt{5}}^{n}}{{2}^{n}\sqrt{5}} ...
Jun23-11 07:35 PM
dimension10
4 6,530
In some exercises I've stumbled upon a function which is denoted \gamma_{m}(n) with m,n natural. I've no idea what is...
Jun23-11 04:36 PM
Hurkyl
3 1,686
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
mathwonk
2 1,368
Limiting ourselves to N... Conjecture: (sqrt (16x + 9) - 1)/2 = y | 2y^2 + 2y - 3 = z^2 for x = a Sophie...
Jun23-11 02:23 PM
ramsey2879
25 7,743
Reading about the general rotation of a single qubit, a rotation of \theta in the horizontal plane and \phi) in the...
Jun23-11 01:06 AM
nomadreid
0 1,911
I need to understand physics (and other) concepts but I'm having trouble visualizing what the equations mean. One...
Jun22-11 10:13 PM
jimgavagan
3 2,121
I am doing my Extended essay about the maths involved in calculating your position using the GPS. I am reading a very...
Jun22-11 03:36 PM
jbunniii
4 4,661
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
Kreizhn
2 1,314
Hello all, I'm a freshman undergraduate (UCLA) and have finished my study lower division calculus (multivar, diff...
Jun22-11 01:07 AM
Bill Simpson
9 3,220
I have two questions and I hope it is acceptable...Seemingly unrelated, though I came to wonder about the first while...
Jun21-11 02:42 PM
micromass
3 1,926
I have noticed something strange when you take the value of sin(pi*10^-n). It approaches pi*10^-n. I have attatched...
Jun21-11 10:53 AM
micromass
3 2,448
Let q be an odd prime power. Let n be the multiplicative order of q modulo t, where t is even and t > 4. What are the...
Jun21-11 09:24 AM
burritoloco
0 1,341
Why is the Trace of a projection is its Rank. Thank you
Jun21-11 03:21 AM
micromass
3 2,967
Let q be an odd prime power. Let n be the multiplicative order of q modulo t, where t is even and t > 4. What are the...
Jun21-11 02:29 AM
burritoloco
0 1,233
I was hoping you guys could help me in understanding some vector spaces of infinite dimension. My professor briefloy...
Jun21-11 12:11 AM
mscudder3
7 4,188
Is it true that every matrix is similar to its transpose? A claim in Wikipedia... (field is alg. closed)
Jun20-11 10:27 PM
arthurhenry
4 1,808
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
Bacle
2 1,487
My understanding of Lie groups is non-existent. But I'm trying to understand if the Leech lattice is a 'lie group?"
Jun20-11 02:55 PM
Aztral
4 1,548
A non-zero alternating tensor w splits the bases of V into two disjoint groups, those with \omega(v_1,\cdots,v_n)>0...
Jun20-11 02:18 PM
micromass
1 1,218
Other than the Eucledean method (1+p1p2p3...)and so on other than this, how do we prove that there are infinte...
Jun20-11 11:46 AM
disregardthat
10 2,968
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
Antiphon
2 2,646
I just read an article (http://www.maa.org/devlin/devlin_06_08.html) saying that multiplication is not repeated...
Jun19-11 06:22 PM
agentredlum
93 15,792
Title says it all really. But basically I'm looking for online info about creating the Leech lattice from the E8...
Jun19-11 03:03 PM
Aztral
0 842
Hi all, I have been trying to gain a deeper insight into quadratic forms and have realised that my textbook makes...
Jun19-11 12:43 PM
lpetrich
14 2,677
Hello, I am trying to solve a Pell's equation X2 + 2Y2 =1 I understand that the (3,2) is a fundamental...
Jun19-11 10:47 AM
RamaWolf
6 2,517
Okay, I know that if I can't get n linearly independent eigenvectors out of a matrix A (∈ℝnxn), it is not...
Jun19-11 06:06 AM
td21
3 1,918
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
mathwonk
2 1,187
Outside of pure mathematics, where is group theory used?
Jun18-11 09:54 PM
mathwonk
6 2,384
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
mathwonk
2 2,950
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
Bacle
2 1,100
i want to extend the set S={(1,1,0,0),(1,0,1,0)} to be a basis for R4. I know I am going to need 4 vectors, so i need...
Jun18-11 04:07 PM
Bacle
6 6,520
Hi all, I have problem with regard to ill-conditioned linear system of solving sets of simultaneous equations using...
Jun18-11 02:29 PM
kaizen.moto
0 1,399
such as some 3D matrix visualization or eigenvalue/singular value things/jordan form? Thanks very much for any...
Jun18-11 10:01 AM
Stephen Tashi
1 1,659

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