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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 36,260
I have a question regarding the Gram-Schmidt process. When solving for the new subspace, is it okay to make a newly...
Oct1-10 12:45 PM
2 955
We have W = 1,v2,v3,v4] v1=i-k v2=i+j+k v3=j+2k v4=2i+j Show that W is a subspace of V3. first, vector 0 is...
Oct2-10 08:37 AM
4 975
I would like to show that (cxb).a = (axc).b in Rn where x denotes the cross product and . denotes the dot product. ...
Oct2-10 08:56 AM
2 1,022
Hello, I read somewhere that the set of unit quaternions identifies the \mathcal{S}^3 sphere. This makes sense;...
Oct2-10 03:17 PM
12 1,963
what is the maximum number of terms can a arithmetic progression of only prime numbers have?
Oct2-10 09:20 PM
2 2,297
Oct3-10 05:26 AM
1 922
Oct3-10 11:13 AM
1 1,060
Hi all, I've been reading up on ways of factorising numbers through the congruence of squares method...
Oct3-10 12:15 PM
1 1,933
Hai friends I am aravind,doing post graduate in computer science .In this thread I explain about the...
Oct3-10 03:39 PM
11 4,474
Sounds great thank you
Oct3-10 04:28 PM
3 1,156
How do we know that the cartesian product of any two groups is also a group using the axioms of group theory?
Oct3-10 05:58 PM
6 2,397
I read the following on the wikipedia page about simple rings ( I do...
Oct3-10 10:32 PM
3 1,144
Lets say I have a 3x3 matrix 'A' and one known eigenvalue 'z' and one known eigenvector 'x', but they don't "belong"...
Oct4-10 12:35 AM
7 1,779
Hello everyone, I need some help with finding norms of the field extension. I feel pretty comfortable when...
Oct4-10 11:08 PM
1 855
Hello everyone. I was going through my Linear Algebra Done Right textbook that threw me off. I hope this forum is...
Oct4-10 11:17 PM
3 5,152
dimension of sl(2,R) = 1*(2*2-1) = 3, is isomorphic to so(2,1) : 2+1 = 3 dimension of sl(2,C) = 2*(2*2-1) = 6, is...
Oct4-10 11:18 PM
2 1,538
What could we say if a matrix is invertible? Could we say that it can span and is linearly independent?
Oct5-10 08:44 AM
1 3,036
Recently when I talked to a professor specialized in number theory, I learned about normal numbers. So the other...
Oct5-10 05:34 PM
8 1,577
Hi, I need to do Interpolation of complex numbers let say z1=x1+i*y1 and z2=x2+i*y2 now I have two approaches:...
Oct5-10 05:42 PM
2 2,975
This should be a simple question for anyone familiar with basic algebraic geometry, but the concept is getting the...
Oct5-10 08:02 PM
5 1,666
consider a vector A A = A(A dir) here A dir is A with hat on...
Oct5-10 11:04 PM
5 1,032
I notice that the trick to define Dirichlet Eta Function can be repeated for each prime number, let p a prime, and...
Oct6-10 04:07 AM
0 993
Preface: I am an electrical engineer studying for the PE exam. I am reviewing power system analysis and have come...
Oct6-10 02:58 PM
2 1,219
like N=5053=163*31 and N=169*37=6253 if we do not know the factors and if we do not want to factor them. They both...
Oct6-10 09:48 PM
6 1,263
I am reading a paper where the author uses colons in the description of groups. Example (not verbatim): "This subgroup...
Oct7-10 10:23 AM
2 2,013
The formula used for linearization is y=(m)(Square root of x) + b correct? How do I find the square root of x if...
Oct7-10 10:36 AM
1 3,354
Hello, it is known that pure-quaternions (scalar part equal to zero) identify the \mathcal{S}^2 sphere. Similarly...
Oct8-10 01:21 AM
10 1,934
Is it true that if a finite group G contains a subgroup of index 2, then there is an element of G with order 2?
Oct8-10 10:08 AM
3 835
Is it possible to write the 2010 numbers from 1 a 2010 in some order so that the 6933 digit number you get is prime?
Oct8-10 07:25 PM
11 1,686
Hello, let's consider, for example, the Clifford algebra CL(2,0) and the following mapping f for an arbitrary...
Oct9-10 03:59 AM
4 1,556
I know about using projector decomposition in diagonalization, but I heard from a friend about finding a 2x2...
Oct10-10 02:21 AM
0 713
I am interested in twin primes and have not been able to find a simple "sieve" type function to calculate them. I...
Oct10-10 09:27 AM
2 2,539
Let G be the group of 2x2 invertible upper triangular matrices and H be the group of 2x2 invertible lower triangular...
Oct10-10 06:26 PM
4 1,710
I saw the following problem on my abstract algebra book (dummit && foote) , I tried to solve it but I couldn't : Let...
Oct11-10 04:03 AM
3 1,770
Is there a tool that spits out a general polynomial formula for an input consisting of a finite sequence, e.g.: you...
Oct11-10 09:38 AM
6 3,610
Hi out there peps, very nice forum! (my first topic) Atm Im dealing with complex numbers, and Ive got kinda problem...
Oct11-10 10:03 AM
2 1,253
so i've been reading jim hefferon's linear algebra book i dont know if anyone on the forum has seen it, but im only...
Oct11-10 11:24 AM
4 943
First it must has char.poly x^2*(x-c), then c must be zero because char. poly and min. poly have the same roots. ...
Oct11-10 03:13 PM
0 1,557
Hello! I've got several sets of data that are all intended to represent the same ideal data set....
Oct11-10 03:21 PM
2 763
I was wondering what would be the largest possible value for a determinant, for a 3 by 3 matrix whose entries can only...
Oct11-10 06:42 PM
3 4,300

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