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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 35,887
Is there an easy way to see if a unitary group is cyclic? The unitary group U(n) is defined as follows...
Apr7-13 03:49 PM
12 2,030
EDIT:( Sorry I meant for the title of this to say conjugacy classes of subgroups of Z X Z) I have a question. I...
Apr7-13 11:11 AM
6 1,213
I was wondering if anyone has compiled a list of AA resources. Recently, I have found that I practically need to learn...
Apr6-13 03:22 PM
2 731
I heard this assertion during a discussion: If two matrices are similar, but one is symmetric and the other is not,...
Apr5-13 08:40 PM
2 649
Is there a generalization for the Chinese Remainder Theorem if the modular bases are not coprime? Or even to some...
Apr5-13 08:53 AM
1 2,392
z = h(x) + ig(x) True or False: By the definition of the complex plane, h(x) and ig(x) will always be orthogonal. ...
Apr4-13 08:44 PM
7 1,230
Can anybody explain me how did the author obtain the third line from the second in document 111.pdf? In the second...
Apr4-13 11:42 AM
0 653
Hi everyone, I am currently dealing with a nonlinear system of coupled equations. In fact I had performed a...
Apr3-13 03:56 AM
5 885
I have solutions for eigenvalues to be λ1=i-1 = √2 e^i(3∏/4) and λ2=i+1 =√2 e^i(∏/4) How do you go from the...
Apr2-13 03:50 PM
4 754
Let T be an operator on the vector space V and let λ1, ..... , λn be it's eigen values including multiplicity . ...
Apr2-13 12:23 PM
9 1,135
How come a square matrix has eigenvalues of 0 and the trace of the matrix? Is there any other proof other than just...
Apr1-13 12:40 PM
3 3,405
Hey, just trying to get my head around the logic of this. I can see that if composition factors are cyclic then...
Mar31-13 11:42 AM
0 942
Is there a general algorithm for taking the presentation of a group and get the permutation generators for the...
Mar30-13 12:31 AM
1 822
Hi, My textbooks say that when a solution, x, is found to Ax=b it has a particular solution, x_0, such that A*x_0=b...
Mar29-13 04:52 PM
6 1,377
I have the following matrix inequality which is nonlinear due to M^TM. In order to transform into an LMI, I apply the...
Mar29-13 05:50 AM
0 589
I've been taught (in the context of Sturm-Liouville problems) that Fourier series can be explained using inner...
Mar28-13 08:14 PM
16 3,193
Can someone tell me why Sum from j=1 to 3 of y_j*(x'_j , x'_k) = (f , x_k) for 1<=k<=3 where (x1,x2) is the...
Mar28-13 06:18 PM
0 513
Is the dual space a V* a sub set of V?
Mar27-13 06:26 PM
12 921
I saw a picture of what it might look like when I was researching it, but I'm confused about something. The picture's...
Mar26-13 07:44 PM
0 523
A forgetful functor ignores structure on a set (under an embedding interpretation) prior to its mapping to another...
Mar26-13 04:38 PM
0 707
Hello All, I was trying to prove that an operator T in a real vector space V has an upper block triangular matrix...
Mar26-13 09:14 AM
0 531
basically i have a problem where i am rotating 1 vector to be parallel to another i get the axis of rotation by the...
Mar25-13 11:37 AM
Ben Niehoff
1 637
This is a problem that a few friends and I came up with while working on an extra-curricular robotics project: ...
Mar25-13 10:47 AM
3 898
EDIT UPDATE so basically I figured this out. it was apparently what i was rotating around. Now i can rotate much...
Mar25-13 03:10 AM
0 585
Suppose we have an nxn matrix A with column vectors v1,...,vn. A is invertible. With rank(A)=n. How do I prove that...
Mar23-13 05:09 PM
4 967
I am curious on how the determinant function determines orientation? I read about in in one of Werner greubs books and...
Mar23-13 02:10 PM
6 1,168
I must apologize if this question sounds dump but if an isomorphism is established between two groups, is it true that...
Mar23-13 02:07 PM
4 899
There is a corollary in our textbook that states "Let G be a group of order 12 whose 3-Sylow subgroups are not normal....
Mar23-13 12:18 PM
1 768
I was a bit confused the last paragraph before "Corollary 4.6.4". It says that we have the isomorphism \alpha : Z_k...
Mar23-13 08:21 AM
2 823
Hello, I'm in an introductory course about quantum computing. My math experience is fairly solid, but not very...
Mar22-13 08:01 PM
2 613
Good afternoon! I am working on a problem, where I at some point have to find the intersection between a polytope...
Mar22-13 05:16 AM
0 541
Let an,m be defined for the non-negative integers n and m such that n ≥ m. an,0 = 1 am,m = m! an+1,m+1 = (m+1)...
Mar21-13 10:13 AM
1 734
Hi everyone. Is there any way to set demands on least square solutions? I have an equation on the form Ax=b,...
Mar21-13 07:59 AM
4 1,038
I think this may be a simple yes or no question. I am currently reading a book Vector and Tensor Analysis by...
Mar20-13 03:49 PM
4 1,510
Claim: If p \in R is irreducible and non-zero, then p is irreducible and prime in R Proof: Let I be the ideal...
Mar20-13 03:44 PM
1 620
it seems to have many different ways to express a determinant, when we are using indices to write vectors and tensors,...
Mar19-13 11:45 PM
1 593
Hello! If anybody has a minute, I'd appreciate a quick look-through of my proof that a finite abelian group can be...
Mar18-13 02:37 AM
4 977
Let A be any real invertible matrix. There exists a non-zero diagonal matrix D such that A^T D A=D. I'm pretty sure...
Mar16-13 12:52 AM
8 1,586
Consider an unbounded self-adjoint operator defined in a hilbert space(its domain isn't the entire hilbert space,of...
Mar15-13 10:28 AM
1 631
There is some theorem along the lines that any category of schemes embeds into a suitable Grothendieck topoi. What is...
Mar15-13 02:45 AM
Jim Kata
1 534

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