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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 36,211
Hi everyone. I am not sure if this problem belongs under the "Linear & Abstract algebra" section but it seemed like it...
Feb17-09 02:19 PM
mathclass
4 4,799
This example appears in a set of notes entitled Geometric Algebra. I cannot follow the first half of the example....
Apr21-07 06:08 PM
matheinste
6 1,379
Help needed to eventually understand Quotient spaces.
Feb12-08 04:23 PM
mrandersdk
8 2,530
Hello all. I wasd beginning to feel at home with vectors and covectors but while trying to fully understand the...
Jun20-07 06:54 AM
matt grime
25 5,039
Hello Everyone. In a thread in this forum relating to a problem on Subspaces I read that as long as a Vector...
Jul1-07 07:12 PM
matheinste
8 3,717
Is there any difference between a vector subspace and a linear manifold. Paul Halmos in Finite Dimensional Vector...
Oct31-08 06:57 AM
HallsofIvy
13 8,689
Hello all. I am in need of a quick clarification. A text I am reading describes an ideal in a ring as 'analogous'...
Aug1-07 07:57 PM
matheinste
7 2,257
Hello all. I reluctantly ask this question because it is probably,as the text states easy, but my desire to clear...
Aug3-07 01:24 PM
matheinste
6 1,691
Hello everyone. I came across the term free vector space in a book on mathematical physics by Geroch but cannot...
Dec30-07 12:08 PM
mathwonk
11 9,933
Hello all. While going back to group theory basics to make sure i understand rather than just know the fundamentals...
Nov4-07 04:36 PM
matheinste
4 3,382
Hello all. I came across this problem in Halmos, Finite-Dimensional Vector Spaces, page 16. Is the set R of all...
Apr5-08 01:41 PM
HallsofIvy
33 11,972
Hello all. Back to basics again. When defining a set of geometric vectors for a vector space of n dimensions how...
Dec11-07 05:39 PM
matheinste
9 1,655
Hello all. I am reading again about free vector spaces over a set. In the Theory of Groups by Kurosh part of the...
Dec24-07 10:50 AM
mathwonk
6 2,133
Hello all I have read about quotient spaces of a vector space in several books and have an understanding of what...
Mar30-08 08:22 PM
matheinste
2 1,428
Hello all. Most modern treatments of the tensor product use equivalence classes to define a quotient space in order...
Feb25-09 11:52 AM
fisicoloko
11 3,586
In several places I have come across what seems to be a standard proof by contradiction that there is no greatest...
Dec6-09 09:50 AM
matheinste
14 6,517
Howdy, I just stumbled on this forum and was hoping someone could help with this proof: If a and b are elements of...
Dec12-04 11:27 PM
MathematicalMatt
3 1,658
in this webpage there is a book about recreational maths in it there is a paradox by raymond smullyan, it's on page...
Nov2-03 08:34 AM
Hurkyl
11 2,661
i read the book "the man who loved only numbers" by paul hoffman, and there is explanation about fermat's test for...
Nov1-03 12:35 PM
Hurkyl
8 3,390
can some one explain to me how is taking the logarithm of euler product gives you -sum(p)+log(s-1)=log? my question...
Dec18-03 12:28 PM
MathematicalPhysicist
2 3,925
i think everyone is familiar to this but i wonder if someone has made his research to study it. what i mean is the...
Feb19-04 07:41 AM
MathNerd
12 2,332
im not trying to be a crank and give you a solution to it but im looking for the proof of Ivan Vinogradov "that every...
Mar2-04 09:07 AM
MathematicalPhysicist
7 4,519
i made a question by myself here it goes: proove that the only solution to p is 3: n^2-1=p where n is a natural...
Mar25-04 09:34 AM
matt grime
5 1,795
in mathworld, they say that conway proved "that Collatz-type problems can be formally undecidable." does it mean that...
Jan4-05 11:07 AM
master_coda
14 3,568
is really the only way of checking which number is divisble by 7 is by modular arithematics?
Jan16-06 12:13 PM
MathematicalPhysicist
12 2,473
i reackon youv'e seen it already, the problem is to rearrange the next numbers in the fixed order: 1 2 3 4 5 6 ...
Jan29-06 12:09 AM
Robokapp
3 2,410
is there some theorem of some sort, that connect the number of divisors of a number to identify if it's even or odd? ...
Apr2-06 12:47 PM
Gokul43201
4 2,837
i'm refering to this:http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX36.html does someone know if...
Apr4-06 01:15 PM
robert Ihnot
2 2,089
i chekced a few perfect numbers with module 6 and, a nice property is that all mod 6 equal 4 (at least for those i...
May7-06 06:04 AM
Muzza
9 1,869
i need to remember when does Ax=B has a unique solution, more than one, and no solution? i think that it has a...
Jun14-06 02:48 AM
doodle
1 1,208
i need to find how many automorphisms are there for the field Q(sqrt2). i am given the hint to use the fact that a is...
Nov30-06 12:10 PM
mathwonk
8 2,084
let V be a vector space and K a nonempty subset of V prove/disprove : K is linear independent set iff for every T...
Feb5-07 07:01 AM
HallsofIvy
11 2,843
i need to prove diprove that there exist matrices A1,A2,...,As such that rank Ai=1 for every i=1,...,s and...
Feb5-07 08:20 AM
MathematicalPhysicist
2 1,483
1) there's given a transformation f:C^n->C^n (C is the complex field), it's known that f is linear on R (real numbers)...
Feb5-07 04:54 PM
matt grime
5 1,858
the question is as follows: gcd(n,10)=1, i need to prove that there exists a k>=1 such that 10^k-1 is divisible by n....
May4-07 01:36 PM
MathematicalPhysicist
15 3,023
i have this matrix: 011 001 000 and i need to find the matrix jordan basis, and jordan form. for the jordan...
May4-07 03:45 AM
MathematicalPhysicist
10 2,686
im given a matrix H from M_n(C) (the space of nxn matrices above the comples field). and we know that for every a in...
Jul10-07 08:55 AM
matt grime
8 1,668
There's a question that asks me to show that there exists a unique linear transformation from: f\otimes g: V_1\otimes...
Jul5-08 02:47 PM
mrandersdk
9 1,444
I know how the rotation matrix looks like in the 2x2 and 3x3 orders, but how does it look in general? thanks in...
Aug1-08 02:56 AM
MathematicalPhysicist
9 8,303
What is the rule of division by 23? Thanks in advance.
Jan24-09 04:57 AM
MathematicalPhysicist
20 3,406

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