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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 34,803
Hi everyone. My first post on this great forum, keep up all the good ideas. Apologies if this is in the wrong...
Nov15-11 05:18 AM
pwsnafu
1 1,742
I have read at a lot of places that in 2D transformations rotation is a combination of scaling and simultaneous shear?...
Nov15-11 04:18 AM
Deveno
3 2,812
Which of the transformations are onto? 1) T:R2 -> R2, where T(x,y) = (5x-y, 0) I don't know if I'm understanding...
Nov15-11 03:47 AM
Deveno
1 1,488
Let Fn = 22n + 1 be the nth Fermat number and suppose that p|Fn, where p is a prime (possibly Fn itself). Show that ...
Nov14-11 10:25 PM
demonelite123
4 2,060
If we take the derivative of n functions that are linearly independent to each other and we write it down like c1f1(x)...
Nov14-11 03:30 PM
AdrianZ
8 2,197
Hi guys, I have a bit of a strange problem. I had to prove that the space of symmetric matrices is a vector space....
Nov14-11 02:12 PM
Rowina
0 929
Do tuples exist which aren't elements of a cartesian product of sets? Can you just write an ordered list of elements...
Nov14-11 09:18 AM
eztum
3 1,406
This is more of a conceptual question more than anything. I've never done any financial modelling, let alone modelling...
Nov12-11 10:32 PM
Stephen Tashi
1 2,981
I have an equation: tr\left\{\textbf{AB}\right\} = \sigma where tr\left\{\right\} denotes the matrix trace. The...
Nov12-11 02:56 PM
weetabixharry
5 1,487
Hello. First, I'd like to apologize because I don't know where to go ask for homework on linear algebra on the forums...
Nov12-11 09:21 AM
sam0617
6 6,095
Hi, I wonder that is there any way to disassemble this operation ((n+2^(n-2))^2 mod 1000000007) without counting...
Nov12-11 07:47 AM
I like Serena
15 3,841
Consider a category C with objects ob(C) and morphisms hom(C). Suppose there is a subcategory D such that ob(D)=ob(C)...
Nov12-11 07:10 AM
tmatrix
0 805
I have heard about the Riemann Zeta function to be some kind of physical partition function..my question is..could we...
Nov12-11 01:31 AM
Mats Granvik
5 3,577
Let A be a nonzero matrix of size n. Let a k*k submatrix of A be defined as a matrix obtained by deleting any n-k rows...
Nov11-11 09:16 PM
Deveno
2 2,671
Hi. I'm preparing the Linear algebra 1 Exam for the first year of Physics University. I find very difficult to...
Nov11-11 04:25 PM
Bacle2
1 2,151
If A and B are both invertible square matrices of the same size with complex entries, there exists a complex scalar c...
Nov11-11 03:48 PM
Grothard
2 1,524
Hello, how to find matrix 4x4 which only contains whole numbers and has inverse matrix with whole numbers only aswell?...
Nov11-11 11:59 AM
Bacle2
10 2,635
I think this is true but not sure how to prove it. Suppose that A and B are both totally unimodular matrices then is...
Nov10-11 11:02 PM
hedgeway
0 854
I was browsing through the Notation section of my favourite book and noticed that symbols were defined for the "sets"...
Nov10-11 01:49 PM
SteveL27
12 4,007
Can anyone tell me how to calculate the discriminant of a general equation of 2 degree in 2 variables,...
Nov10-11 09:26 AM
Stephen Tashi
3 2,920
I tried googling this first and of course looked at my notes but the questions asked pertaining to dimensions were...
Nov10-11 08:44 AM
sam0617
4 1,629
If you have a matrix that is a combination of a diagonal, upper, and lower matrix - what is the best way to solve it?...
Nov10-11 04:44 AM
weetabixharry
1 2,386
Hello, I'm currently self-studying "An Introduction to Convex Polytopes" and I'm having some trouble understanding the...
Nov10-11 01:45 AM
Caramon
2 1,608
I have a question about the exterior product. Is it true that \mathbf{a}\wedge\mathbf{b}=|| \mathbf{a}\times...
Nov10-11 12:50 AM
chiro
7 1,483
In an example in my algebra text, (from the section on unique factorization domains) it is describing the ring...
Nov9-11 08:06 PM
alexfloo
1 1,059
I've been stuck on this problem for so long it's getting ridiculous. Please help! I have a complex matrix,...
Nov9-11 05:53 PM
weetabixharry
6 2,367
Hi all, it is of course true that every linear map between two vector spaces can be expanded by means of the...
Nov8-11 11:11 AM
ivl
1 1,810
Hi, I'm not sure this should go in homework of here as this was a test question, but the question its self isn't a...
Nov8-11 07:28 AM
HallsofIvy
14 1,598
I came accross this question. Is the group (ℤ/34/ℤ)x cyclic? We haven't discussed the theorem in class that any units...
Nov8-11 02:03 AM
Bachelier
2 1,146
T: Mnn => R, where T(A) = tr(A) Attempt: 1) T(kA) = tr(kA) = k tr(A) = k T(A) 2) T(A+B) = tr (A + B) =...
Nov7-11 10:30 AM
Deveno
1 1,509
I am dealing with a problem,which can be formulated Ax=B,in the first place I wanted to solve it with conjugate...
Nov7-11 07:40 AM
AlephZero
1 891
Hi guys So I'm studying for my test tomorrow and I understand how to find the dimensions of ColA and NulA, but what...
Nov7-11 02:37 AM
Deveno
5 1,495
Hello! I was just thinking, say, I have a plane with the equation x + 3y + 2z = 0. How would I go about finding...
Nov6-11 06:08 PM
HallsofIvy
1 937
Let K1={a + (2^0.5)*b} | a,b rational numbers}, and K2={a + (3^0.5)*b} | a,b rational numbers} be two fields with the...
Nov6-11 04:52 PM
Deveno
1 871
Hello, Does anyone know if this makes sense or is usable? I've only been able to describe it through a graph....
Nov6-11 09:48 AM
elegysix
4 2,054
if |G| = n . And G has 2n-1 subgroups, prove G = <e> or it is isomorphic to Z2. I am thinking I need to show that n...
Nov5-11 07:19 PM
Deveno
11 3,334
After long and careful search on the web and in literature, I could not find the solution of the following problem....
Nov5-11 06:13 PM
Ulam
5 1,995
A statement in a book of analysis I have says: (Q,+, .) is a commutative ring with an identity element. I assume...
Nov5-11 04:01 PM
bentley4
12 1,446
About two years ago, a friend of mine published his licentiate thesis in mathematics. As an non-mathematician I...
Nov5-11 12:10 PM
Guffel
0 1,074
Hey guys So the problem I'm having here is spans! I know that a basis of a vector space is a linearly...
Nov5-11 08:55 AM
HallsofIvy
5 3,141

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