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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 35,734
It's been some time that I've been studying abstract algebra and now I'm trying to solve baby Herstein's problems, the...
Sep20-11 11:07 AM
micromass
3 1,522
can anyone please explain to me what a spanning set is? i've been having some difficulty with this for a long time and...
Nov3-11 07:51 PM
disregardthat
3 2,797
This is the problem: Suppose A\in\mathbb{R}^{n\times k} is some matrix such that its vertical rows are linearly...
Oct6-11 09:52 AM
jostpuur
3 1,894
To determine if a matrix is invertible or not, can we determine this by seeing if the determinant of the matrix is...
Sep30-11 11:50 PM
Bacle
3 1,390
Here is a bilinear map φ of two vector spaces V₁ & V₂ into another vector space N with respect to the bases B =...
Oct10-11 12:23 PM
lavinia
3 1,726
A graph can be represented by an adjacency matrix but how is that a real mathematical matrix and not just a table? A...
Oct2-11 10:07 AM
AlephZero
3 1,899
Let S be a subring of the ring of integers ℤ. Show that if 13 ∈ S and 1000 ∈ S, then S equals ℤ. I'm thinking we...
Oct4-11 08:42 PM
Bachelier
3 1,025
Now, I can show that if n is prime then Z/Zn is a field a = a b = an-2 a*b = an-1 = 1 (mod n) --> Fermat's...
Oct14-11 11:45 AM
General_Sax
3 1,986
Hello all, I have a problem to define a set of natural numbers that meet the following equation: m2+1\equiv0 ...
Sep29-11 03:14 PM
naoufelabs
3 2,039
Why is it that a metric space (X,d) always has two clopen subsets; namely {0}, and X itself? Rudin calls it...
Oct19-11 10:19 PM
Deveno
3 1,827
Question about linear transformations if you have a matrix such as | 5 6 9 | | 5 0 3 | | 9 -3 -7 | Can it...
Sep20-11 10:26 AM
HallsofIvy
3 1,158
I've been googling but I haven't found anything useful. I am trying to understand how multiplying a matrix (or object...
Sep21-11 04:07 AM
Simon_Tyler
3 1,338
Let F_n and F_n+1 be successive Fibonnaci numbers. Then |(F_n+1)/(F_n) - Phi | < 1/(2(F_n)^2) Where Phi is the...
Oct18-11 03:14 PM
Matt Benesi
3 1,817
Hi guys! I need to solve a matrix. I have 3 equations, 3 unknowns, straightforward stuff. And I know it's...
Oct18-11 07:14 PM
jasonRF
3 1,724
\frac{d}{dx}f(x)=\frac{d}{dx} how to get this derivative, what is the answer? is there textbook describe it?
Oct24-11 09:39 AM
HallsofIvy
3 1,028
How would one normally solve this type of equation x^a = b (mod n) Is there any trick to solve it if I know that...
Sep23-11 02:15 AM
Xitami
3 2,487
There exists none. What's the easiest way to prove this? Can we state that all elements of ℤ are in ℤ but not the...
Oct6-11 02:20 PM
Deveno
3 1,254
Hi, All: Given a quadratic form Q(x,y) over a field of characteristic different from 2, we can find the...
Aug12-11 12:14 AM
Bacle
3 2,261
It is well known that the Harmonic Series diverges (1/1+1/2+1/3+1/4+...), but that the series converges. In the...
Aug17-11 09:48 PM
micromass
3 2,229
I took an Intermediate Linear Algebra course all last year (two semesters worth) and we covered the CDT. My professor...
Aug19-11 05:10 PM
Kindayr
3 2,517
In my lecture notes, the lecturer describes the column space of matrix A as the vector space spanned by the columns...
Aug20-11 05:58 PM
micromass
3 1,246
I've got a question and I really need the answer! Why 10-adics are not a field? And generally, How can you be sure...
Aug24-11 12:30 AM
Citan Uzuki
3 2,193
Hello i have this matrix \in Z mod 7, M = \begin{pmatrix} 0&6\\ 5&0 \end{pmatrix} always modulo 7 in Z. I found...
Aug24-11 06:40 AM
HallsofIvy
3 1,653
This is going to be kind of a long post, and I'm citing the author because it's directly from a textbook, but I'm...
Aug29-11 03:56 PM
blueberryfive
3 2,847
Hi, I have a problem understanding the difference between Cartesian product of vector spaces and tensor product....
Sep5-11 05:26 PM
mathwonk
3 1,698
Hi, just curious as to whether we can map any 2-planep: ax+by+cz=d into any other 2-plane p': a'x+b'y+c'z=d' by...
Sep8-11 01:00 PM
micromass
3 1,330
show that the square of any odd integer is odd, use this fact to justify the statement "if p2 is even , then p is...
Sep12-11 05:47 PM
Amergin
3 1,169
I just can't figure out how you arrive at having a diagonal matrix consisting of Jordan blocks. Going by Lang, a...
Sep14-11 05:40 PM
sponsoredwalk
3 1,614
I'm guessing greater than but I'm not too sure. I need a proof on this so I can be assured of it and then use the...
Sep14-11 04:17 PM
AlephZero
3 3,081
Is it possible for two planes to meet in a point instead of in a line?
Oct20-11 10:53 PM
chiro
3 1,166
When studying complex numbers/vectors/functions and so forth you constantly encounter the idea of an inner product of...
Oct23-11 10:17 AM
Fredrik
3 1,074
So i have 3 vectors: a= b= c= How do I calculate the L in order to make these vecotrs linearly dependent? ...
Oct24-11 12:49 PM
gotmejerry
3 648
1. Problem: Suppose a is a group element such that |a^28| = 10 and |a^22| = 20. Determine |a|. I was doing some...
Oct26-11 08:38 PM
micromass
3 2,400
Hi, I have just begin with Linear Algebra. I came across cosets and I dont understand what is the difference...
Oct30-11 12:31 PM
Deveno
3 1,563
Hello I am trying to solve a problem that involves "the plane y=z". How exactly should I think of this plane? It's...
Oct30-11 12:48 PM
Deveno
3 889
I came across this while doing some research. Can someone help me understand this concept. x^2+1 has a root in Zp, ...
Oct29-11 09:56 PM
Bachelier
3 1,457
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 1,430
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 2,968
As we know grad F (F surface) is in normal direction. But we also have (grad F(r)) x r = F'(r) (r) x r = 0 this...
Nov16-11 10:10 AM
seshikanth
3 1,071
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 2,858

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