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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 33,911
How to detect redundant equation from a system of nonlinear equation? It means how to find out a system of nonlinear...
May26-12 06:02 AM
algebrat
3 2,583
Are there any nice applications of the Cayley Hamilton Theorem. I am looking for a real life application which would...
Jun22-12 02:08 AM
marygoss
3 11,173
Consider the space of all polynomials in n variables of degree at most d. The dimension of that space is C(n+d,d). How...
Jul15-12 06:29 AM
chiro
3 2,439
I am wondering how to organise all of those concepts in my head. should i think of it like: subspace > vectorspace...
May26-12 08:12 AM
algebrat
3 1,502
Hi: I am a newbie to linear algebra; I have a problem about vector space and subspaces. How to distinguish these...
May17-12 05:44 PM
applechu
3 1,024
Hello, The formulation of the question says: Show, using congruences and disjunction of cases, which,for all...
May17-12 08:09 PM
ramsey2879
3 2,149
Is it correct to say that any order 4 group is only isomorphic to either C4 or C2+C2 ? where C4 is the order 4...
May23-12 03:10 PM
lpetrich
3 1,713
There is a difference between the multiplication op in the Field of Reals and the Scaling op in the Set of Vectors. In...
May23-12 04:57 PM
SteveL27
3 1,402
good day! i need to prove that the alternating group An is a normal subgroup of symmetric group, Sn, and i just want...
May26-12 07:34 PM
haruspex
3 1,156
I'm doing a particular form of regression that gives a eigenvector and matrix for the solution. I'm using two matrix...
May31-12 08:51 PM
chiro
3 1,250
Ok, to start off I have been examining the structure of polynomials. For instance, consider the general polynomial ...
Jun1-12 02:38 PM
galoisjr
3 1,234
i'm trying to find a version of PARI or PARI/GP or a comparable number theory program that will run on my MacBook Pro....
Jun16-12 01:19 AM
TylerH
3 2,119
What is the LaTex and infinite sum for 1-2-1/2+3-1/2-4-1/2+5-1/2 . . . Does it converge anyway? I am too old for...
Jun5-12 04:16 AM
Xitami
3 2,137
Show that a rotation by θ followed by a rotation by φ can be expressed as either two consecutive rotations, or one...
Jun13-12 03:47 PM
HallsofIvy
3 1,266
Is there such a thing as a "feral polynomial" ? Saw it mentioned on an Internet forum where someone claimed to be...
Jun16-12 11:52 AM
HallsofIvy
3 964
Here's a question. Pi is said to be the ratio of a circle's circumference to its diameter. If this is the case, what...
Jun21-12 08:23 PM
SteveL27
3 2,248
I'm reading through a multivariable calculus book and it starts off with some linear algebra. It defines vector...
Jun23-12 07:29 PM
jcsd
3 1,398
Exercise #17 in Linear Algebra done right is to prove that the dimension of the direct sum of subspaces of V is equal...
Jun25-12 01:02 PM
DonAntonio
3 1,357
Hello, I am looking at the proof (Theorem 2.5 (b) Apostol) of $$ \phi (mn) = \phi(m) \phi(n) \frac{d}{\phi(d)} $$...
Jun28-12 06:03 PM
DonAntonio
3 1,745
Assume u:R\rightarrow C^n and define shift operator S(\tau) with S(\tau)u(t)=u(t-\tau) and truncation operator...
Jul1-12 02:58 AM
Einj
3 902
Proposition: \sum_{i=0}^{p-1} (\frac{i^2+a}{p})=-1 for any odd prime p and any integer a. (I am referring to the...
Jul2-12 04:21 PM
DonAntonio
3 1,638
I have a large real symmetric square matrix (with millions of rows/columns). How can I identify the sets of rows that...
Jul18-12 10:26 AM
Big Data Alan
3 1,732
Disclaimer: Sorry if this question is off-topic, I really don't yet know where it "belongs". I wrote a program that...
Jul7-12 03:22 PM
matthew180
3 1,283
For approximately the last two years, I have been working off and on for a proof of whether Brocard's problem was...
Jul9-12 02:25 PM
Millennial
3 2,449
Can someone please explain why 80 mod (-11) is -8Ö? Why isnít it 3? b = aq + r 80 = (-11)q + r 80 = (-11)(-7) + 3...
Jul15-12 08:25 AM
HallsofIvy
3 1,642
I'm self-studying representation theory for finite groups using "Group Theory and Quantum Mechanics" by Michael...
Jul19-12 04:27 PM
LastOneStanding
3 1,152
Say we complex structure J on a space with even dimension. Is there a trick to finding another complex stucture I that...
Jul24-12 09:04 PM
Ben Niehoff
3 961
Def: A low discrepancy sequence is a uniformly distributed sequence with minimal discrepancy, O(logN/N). Question:...
Aug2-12 03:26 PM
mehr1methanol
3 1,380
Suppose that we have a cross-product of vectors. a ◊ b = c Now suppose that we have an orthogonal matrix M. Is...
Jul23-12 07:16 PM
micromass
3 1,817
Say I have a system of equations of the following form: a_1 A^2 + b_1 B^2 + c_1 C^2 + d_1 = f_1 a_2 A^2 + b_2 B^2...
Jul27-12 06:56 AM
HallsofIvy
3 851
Assume P is a symmetric positive-definite matrix, and S to be a diagonal matrix with all its diagonal elements being...
Aug1-12 02:26 AM
chiro
3 1,204
I am having trouble understanding the permutations of a finite set in general. I want to know what it may be used for,...
Aug3-12 01:59 PM
marschmellow
3 1,120
Hello everyone, this nxn matrix arises in my numerical scheme for solving a diffusion PDE. M =...
Aug1-12 09:09 AM
Jonnyb302
3 888
Let us take the most mainstream irrational out there, (Pi). Now write (Pi) as: 3. 14159265... Let us number...
Aug5-12 07:34 AM
mfb
3 1,783
This is very weird, but I found an inconsistency in the application of Cramer's Rule for a 3x3 simple linear matrix. ...
Aug10-12 10:03 AM
DonAntonio
3 1,019
Suppose we have a finite dimensional inner product space V over the field F. We can define a map from V to F...
Aug11-12 08:13 PM
dEdt
3 1,215
The isomorphism of ℝ5 and P4 is obvious for the "standard" inner product space. The following question arise from...
Aug18-12 09:58 PM
chiro
3 1,039
Can any one clarify the concepts of zero vector and zero scalar? -Devanand T
Aug18-12 10:13 AM
Fredrik
3 2,248
Hello fellas. I have this formula that encodes data: OUTPUT = (Data * 7) + (Data * 2) + 8 So in this case, if...
Aug14-12 06:11 AM
chiro
3 793
Let p be a prime. Let H_{i}, i=1,...,n be normal subgroups of a finite group G. I want to prove the following: If...
Aug16-12 10:10 PM
moont14263
3 1,139

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