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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
1 35,972
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
3 1,535
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
3 1,910
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
3 1,402
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
3 1,737
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
3 1,921
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
3 1,033
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
3 2,005
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
3 2,058
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
3 1,844
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
3 1,168
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
3 1,355
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 1,832
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
3 1,738
\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
3 1,036
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
3 2,504
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
3 1,267
Esteemed Algebraists: Please help me understand better the definition of a transvection. Let V be a...
Jul28-11 10:28 PM
3 1,772
Hi, I have a rotated frame (new matrix, T(x,y, z)) and the original frame (old matrix T(X,Y,Z)). I want to use this...
Aug4-11 02:11 PM
3 2,903
The book I use for linear algebra explains that the motivation for defining a vector space has to do with the Gauss'...
Jul27-11 04:01 AM
3 2,029
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
3 2,275
Hello, After a theorem stating that the product, sum, etc of two elements of a field extension that are algebraic...
Jul27-11 05:55 PM
3 2,198
Is the following theorem true: Theorem: Suppose a, \, b \in \mathbb{R}^k. If |a| + |b| = |a + b| , then |a| and ...
Aug4-11 10:53 PM
3 1,698
I think this is a pretty simple question. I need a transformation that will take a Column vector e.g.: <a,b,c> and...
Aug4-11 10:35 PM
3 2,107
I've been playing with a computational system that represents numbers in their simple continued fraction form. That...
Aug10-11 11:17 PM
3 2,931
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
3 2,247
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
3 2,533
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
3 1,255
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 2,207
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
3 1,671
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
3 2,865
Hi, I have a problem understanding the difference between Cartesian product of vector spaces and tensor product....
Sep5-11 05:26 PM
3 1,717
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
3 1,343
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
3 1,181
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
3 1,628
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
3 3,102
Is it possible for two planes to meet in a point instead of in a line?
Oct20-11 10:53 PM
3 1,177
When studying complex numbers/vectors/functions and so forth you constantly encounter the idea of an inner product of...
Oct23-11 10:17 AM
3 1,083
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
3 652
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
3 2,417
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
3 1,468

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