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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 35,962
Hey I have a problem in which I need to show that a linear transformation is an isomorphism with another linear...
Oct20-13 04:10 PM
1 621
I'm slightly confused by definition of normalises. It's shown in my notes that for two subgroups H, K of G we have...
Oct19-13 01:39 PM
0 569
Hi. I dont understand the following proof. Lemma Let p be a prime number and 1<=k<=p-1, then: {p \choose k}...
Oct19-13 12:59 PM
6 652
So I been working with quaternions as you all know. I get them basically, but to really understand their rotation...
Oct19-13 12:53 AM
Simon Bridge
1 644
Consider two square matrix A,B each specifying a parallelopiped by three different vector. The x, y, z components are...
Oct18-13 12:11 PM
14 1,134
I know that 3 x 3 determinant gives the volume of a parallelopiped, but how come after the row operations also it's...
Oct17-13 09:00 AM
3 890
Is the title statement true? Was doing some studying today and this caught my eye, haven't looked into linear...
Oct16-13 10:12 AM
3 2,512
Correct me if I'm wrong here but it is my understanding that vector spaces are given structure such as inner products,...
Oct15-13 10:32 PM
15 8,028
Let A be a Hermitian operator with n eigenkets: A|u_i\rangle = a_i |u_i\rangle for i=1,2,...,n. Suppose B is an...
Oct15-13 04:40 PM
6 1,361
Please do not be offended by my literary style. I find thinking about mathematical problems in such a way helps me...
Oct15-13 07:01 AM
9 5,163
I'm trying to really solidify my maths knowledge so that I'm completely comfortable understanding why and how certain...
Oct14-13 02:33 PM
6 2,598
Hi, I've Read an Article That Says: If: EQ.1:...
Oct14-13 07:10 AM
2 2,275
The following inequality can easily be proved on ##ℝ## : ## ||x|-|y|| \leq |x-y| ## I was wondering if it...
Oct12-13 08:28 PM
2 1,059
How would I construct noncyclic groups of whatever order I want? For example g is order 8.
Oct12-13 08:05 PM
5 6,205
Hi all, Suppose I have a system which can be described using something like: y(t) = a_1 x(t) + a_2 x^2(t) +...
Oct10-13 08:37 PM
6 1,111
Hi Lets say I have a vectorspace in Rn, that is called V. V = span{v1,v2,..... vk} Is it then possible to...
Oct10-13 07:56 PM
7 5,805
Hey all, I'm trying to understand the Capon Method for some reading into MIMO radar and went to the original source ...
Oct10-13 06:47 PM
6 2,148
This question broadly relates to principle component analysis (PCA) Say you have some data vector X, and a linear...
Oct10-13 12:41 PM
4 1,425
Hello. So today in class, we talked a bit about <g> as the set of all integer powers of g. Made enough sense. Then we...
Oct10-13 03:41 AM
1 638
Consider the 4x4 matrices A = (1 2 3 4) (5 6 7 8) (9 10 11 12) (13 14 15 16) B= (1 2 3 4)
Oct9-13 03:36 PM
1 666
According to wikipedia, absorption is an axiom for a boolean algebra. This seems incorrect to me, since I believe...
Oct9-13 02:48 PM
3 837
Hey everyone Let's say I have two generators, a and b, with the following relations: a^{5}=b^{2}=E...
Oct8-13 07:40 PM
26 3,722
Hey guys! Basically, I was wondering how to prove the following statement. Ive seen it in the Hamermesh textbook...
Oct7-13 07:47 PM
4 1,830
hey all well the title says it all. if i want to take the cross product of two matrices, how do i do it? any help,...
Oct7-13 06:42 PM
3 1,062
Hi, I was wondering what the quickest set of vectors in higher dimensions, say ℂ5? I have a set of vectors {...
Oct5-13 11:32 AM
11 7,893
I posted this question over at the QM page, but I realized...
Oct4-13 10:53 PM
3 1,727
hey all! does anyone recommend any books or websites that cover tensor (matrix) properties and explanations of the...
Oct4-13 01:21 AM
0 1,452
Hello, How am I to find then number of independent equations in a set using matrix techniques? Thanks
Oct2-13 12:09 AM
5 2,497
Suppose that some infinite set S spans V. Then this means every vector in V is expressible as some linear combination...
Oct1-13 05:16 PM
3 1,410
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 9,459
I'm having some set theoretic qualms about the following argument for the following statement: Let V be a vector...
Sep30-13 10:42 PM
11 3,756
Is there any finite dimensional Lie algebra that is not isomorphic to any of the subalgebras contained in GL(n) ?
Sep29-13 10:49 AM
1 862
I am curious: if f and g are (complex) orthogonal functions, are f* and g also orthogonal? (* denotes complex...
Sep29-13 10:27 AM
2 764
okay so I know that the area of the triangle is half the area of the parallelogram, ill try using pictures because...
Sep29-13 09:50 AM
1 1,226
hello everyone.. if we have a function y=f(x) then in-order to prove linearity we try to justify according to...
Sep28-13 04:55 PM
4 884
given an sop form of a multi variable boolean expression, how to judge if it is linear or not? is (x or y) linear? ...
Sep27-13 05:22 PM
5 1,929
If AB is invertible, then A and B are invertible for square matrices A and B. I am curious about the proof of the...
Sep27-13 02:57 PM
14 8,775
Hello, Just discovered this forum as I'm so intensely curious about this question I sought out just such a place! ...
Sep24-13 03:12 PM
2 1,415
In his interesting book "Moonshine beyond the Monster", Terry Gannon proposes the interesting thought He notes...
Sep22-13 06:37 PM
0 1,301
I am not sure that this is the correct forum for this question. I have multiple sets of 3, 3D (x, y, z) points in...
Sep22-13 01:17 PM
Stephen Tashi
4 1,404

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