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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 35,947
Hey, I have a set of quadratic equations in the form of: ax^2 -bxy + cy^2 = d ax^2 -bxz + cz^2 = d ay^2 -byz +...
May11-11 01:43 PM
20 10,001
Can you help me with this problem: if a^2 divides b^2, show that a divides b. This was a homework question that I...
Oct24-09 05:42 AM
23 9,995
simple problem... 3x = 1 (mod 16), find all possible values of x mod 16 so this is what i've come to: 3x = 1 +...
Mar1-08 04:41 PM
7 9,972
Hello, I have searched through out the internet but I couldn't find any information about the origin of Pascal...
Jul12-08 03:20 AM
7 9,968
Hey all! I am working on this and got confused. Any help at all would be much appreciated! Determine the kernel...
Dec14-09 10:50 AM
6 9,933
Hi all! This looks a pretty nice forum. So here's my question: How do I find/show a basis or orthogonal basis...
Sep25-06 01:31 PM
4 9,908
hi all this is the general problem X\ddot{}+AX\dot{}+BX=0 let A, B,X be 2*2 matrices its application is in...
Mar30-08 01:14 AM
6 9,903
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
11 9,893
I am really confused on this topic. can you give me an example and explain how you found, pleaseee! for example,...
Jul28-10 02:41 PM
14 9,883
how do you prove that if v is an element of V (a vector space), and if r is a scalar and if rv = 0, then either r = 0...
Mar30-04 05:27 AM
matt grime
5 9,810
I've done some more work on my package, adding decompositions of representation powers. It...
Apr17-14 11:59 PM
40 9,804
Here it is... 1/3= .33333333333........... 2/3= .6666666666......... so 3/3= .9999999999.......
Oct8-05 08:03 AM
3 9,788
I am trying to find the Nth power of a general 2x2 real matrix. This seemed simple at first, but I am running into...
Dec25-09 09:24 AM
4 9,756
Please excuse the lack of latex, I'm in somewhat of a hurry and I do not have the time to lookup the latex syntax for...
Mar18-05 03:05 PM
3 9,745
Someone please help me show that (uv)^n= Summation {u^(i)v^(n-i)} where i=0 the starting point and n is the ending...
Mar3-04 09:31 PM
Ed Quanta
18 9,661
Hello I recall, I think, that there is a lemma wich states that a 2x2 symmetric matrix can be diagonalized so that...
Dec28-11 06:52 AM
5 9,638
Hi, I recently became interested in some number theoretical questions. I have actually never really studied it...
Sep11-08 09:08 PM
27 9,631
How can you show that an arbitrary n \times n matrix has n linearly independent eigenvectors? What if all you know...
May4-09 07:54 PM
3 9,627
Let V be a vector space over the complex field. If V has an inner product <\cdot,\cdot>, and ||\cdot|| is the...
May21-10 02:12 PM
1 9,622
Springer is having their annual Yellow Book sale and I was going to pick up an algebra text to supplement Dummitt and...
Oct15-06 01:27 PM
7 9,592
I need help proving the following: 1 A non-square matrix cannot have both a left and a right inverse 2 If a...
Nov4-07 01:18 PM
2 9,584
Is any formula that produces nth prime ? if not visit this web site
Jul18-08 11:49 PM
48 9,579
If A and B are idempotent(A=A^2) and AB=BA, prove that AB is idempotent. this is what i got so far. AB=BA...
Oct15-07 03:02 PM
9 9,547
Hello, I am having trouble understanding groups in my group theory class. I am not confident on how to approach the...
Oct29-03 06:38 PM
4 9,518
Hi, Is there a formula to do this? The textbook just says to "reverse" the action of T to get T^-1 (T inverse). Can...
Jul15-05 09:30 PM
7 9,494
hi that day, a friends of mine asked me to find out the last digit of 3^999. i knew that i have to find out 3^999 mod...
Apr9-06 08:22 AM
8 9,493
I'm stuck on the following problem: Describe the span of the vectors u1 and u2 in R^3, where u1 = (1, 1, 1),...
Jun30-05 11:05 PM
6 9,485
So I'm considering dimensions of real vector spaces. I found myself thinking about the following: So for the...
Mar4-08 10:54 PM
1 9,481
given that 2 matrices have the same eigenvalues is it necessary that they be similar? If not, what is the connection...
Apr22-11 06:20 AM
16 9,473
Hi, this is my first post here, so bare with me. So I need to compute the eigenvectors of a large matrix...
Jul17-08 06:48 PM
9 9,459
I am currently taking a number theory course. The professor who teaches the course is very well known in his research...
Oct1-13 02:58 PM
10 9,456
Hi, I'm trying to solve the following matrix equation: XAX' = B where A,B are known...
Aug11-05 03:21 PM
0 9,450
Do you think you could do vector operations in polar coordinates?
Oct29-04 01:39 AM
James R
2 9,447
1. The problem statement, all variables and given/known data A set of objects is given, together with operations of...
Nov2-07 10:20 AM
36 9,444
Hi, I have forgotten the formula for calculating the second norm of matrix. Does anyone know the formula? Regards,...
Sep17-04 12:31 PM
2 9,418
Hi,I am a Chinese sophomore major in software engineering.I am reading Artin's Algebrarecently and have come across...
Sep8-06 06:01 PM
6 9,406
Alright. As stated in the title above. So, a subspace is a set of vectors that satisfies: 1) It contained the zero...
Mar8-09 04:24 PM
8 9,356
I just have one question about the proof. Why does (p-1)!a^{p-1}=(p-1)!\pmod{p}? It seems like it would be true if...
Sep10-05 08:54 PM
5 9,337
I do not know if this counts as number theory, but I came to this question while studying number theory, so I post...
Mar11-08 01:29 PM
11 9,333
Hi there:) I found a quick formula for calculate perfect numbers. T(v)={{*}^2}/128 - {*}/16 T(v-1) is the...
Jun27-07 09:34 PM
9 9,324

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