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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
micromass
1 35,956
If A\in\mathbb{C}^{N\times N} is some complex matrix, is there anything we could say about the determinant of the...
Dec22-12 08:15 AM
sfn17
2 5,323
Hi, I was playing with Riemann zeta function on mathematica. I encountered with a quite interesting result. I iterated...
Dec22-12 09:48 PM
Jeff Cook
10 2,091
Let B={b1,b2} and C={c1,c2} be basis. Then the change of coordinate matrix P(C to B) involves the C-coordinate vectors...
Dec19-12 10:20 PM
bonfire09
2 1,030
Apart from simplifying matrix powers, why do we want to diagonalize a matrix? Do they have any appealing application...
Dec22-12 06:03 PM
marxLynx
4 1,281
I know that we say two representations R and R' of a group G is equivalent if there exists a unitary matrix U such...
Dec21-12 07:51 PM
micromass
2 817
Eigen values of a complex symmetric matrix which is NOT a hermitian are not always real. I want to formulate...
Dec19-12 12:00 PM
Robert1986
14 2,165
Hello everyone, first time poster, long time reader here! I'm an ex-math major and while I'm no longer pursuing a...
Dec21-12 04:15 PM
johnqwertyful
5 1,086
Hello Could anyone give an intuitive explanation of the determinant? I know mostly what the determinant means and I...
Dec19-12 12:26 PM
mathwonk
4 1,066
Hey all, I have been playing around with a special type of matrix and am wondering if anyone knows of some literature...
Dec30-12 11:21 PM
orthogonal
4 1,475
I am reading linear algebra by Georgi Shilov. It is my first encounter with linear algebra. After defining what a...
Dec21-12 06:23 PM
Fredrik
5 1,223
Getting ready for linear algebra exam. One question that I got right but not exactly sure why is this: ---...
Dec21-12 03:38 PM
Frogeyedpeas
4 1,096
I have been trying to prove the following result: If A is real symmetric matrix with an eigenvalue lambda of...
Dec22-12 04:54 AM
matqkks
2 1,050
What is the best way of introducing singular value decomposition (SVD) on a linear algebra course? Why is it so...
Dec22-12 03:19 PM
Stephen Tashi
2 763
Imagine we have two operators A and B on a complex hilbert space H such that: \psi = (AB-BA) \psi=c \psi \ \ \ \...
Dec22-12 10:42 PM
micromass
6 1,115
Prof. Hugh Montgomery has been quoted as saying that it appeared that, if the Riemann hypothesis is true, the...
Dec23-12 10:37 AM
nomadreid
0 870
Hello, I have a simple(or not?) math problem: I have equations of 3 lines in R3 trought the origin: line l1: ...
Jan1-13 08:12 PM
chiro
5 1,393
Hello, I was wondering, why is the vector projection useful in the way that it is presented? Why isnt just the...
Dec27-12 03:30 AM
Stephen Tashi
12 2,231
Question is : If m,k,n are natural numbers and n>1, prove that we cannot have m(m+1)=kn. My attempt : Using...
Dec27-12 12:16 PM
mathwonk
16 3,007
I have an equation (constraint) which I wish to solve explicitly in terms of gd (or more precisely a scaling factor of...
Dec25-12 02:42 AM
james1234
1 863
Video illustration Hello, Me and a friend, David Barrack, are non-mathematicians but we've been having fun...
Dec25-12 11:34 AM
micromass
2 2,051
I was looking for a hint on a problem in my professor's notes (class is over and I was just auditing). I want to...
Dec28-12 06:42 AM
sammycaps
12 1,309
The logic that odd composite with least difference will be factored easily and large difference would factored hardly...
Jan1-13 09:30 AM
mfb
4 1,651
I've got a general question about Lie algebras, which is basically this: Q: What is there to be said about the Lie...
Dec27-12 01:10 AM
Couchyam
0 761
This may be a very silly question, but still apologies, I read in Sheldon Axler, that the inner product of two...
Dec27-12 07:31 AM
vish_maths
3 858
The book I am going through says this : The below proposition is false for real inner product spaces. As an...
Dec28-12 06:46 PM
chiro
3 1,002
Is there any algorithm to form a magic square of any size with a desired magic sum ? Also can we make a magic square...
Dec30-12 08:09 AM
RamaWolf
6 2,130
Hi All, I have a hard time answering the following. I need some help. Let Z={a,b,c,d,e,f} and let X denote the...
Dec30-12 01:31 PM
laptopmarch
1 752
Theorem : if S ={ v1 , .... , vn} spans the V.Space V , L={w1 , .... , wm} is set of linear independent vectors...
Jan1-13 07:55 PM
mathwonk
10 1,564
Suppose that a = aBc where a and c are vectors and B is some matrix that changes as time "continuously" goes on -...
Dec31-12 04:20 AM
dotiozeros
0 807
Consider an m x n table containing single digits 0 to 9. So each cell contain the digits 0 to 9. My goal is to make...
Jan3-13 11:01 AM
mfb
7 2,256
Hello everyone, I found that you're actively discussing math problems here and thought to share my problem with...
Jan1-13 03:33 AM
phd_student
0 1,017
Hello everyone! I'm a 1st grade student in a slovenian high school. Recently, I've became very intrested in numbers...
Jan6-13 09:22 PM
skiller
11 2,354
Hi. Define a linear mapping F: M2-->M2 by F(X)=AX-XA for a matrix A, and find a basis for the nullspace and the...
Jan2-13 11:59 PM
nickthegreek
2 925
I'm trying to compute the complexity of the quadratic program: $$\displaystyle\min_{\mathbf{X}} (\mathbf{X^TQX +C^TX})...
Jan3-13 08:41 PM
lavinia
3 770
Why do we have x-axis perpendicular to y-axis? Why not 45 or something else? Even if we keep any other angle other...
Jan5-13 12:16 PM
Studiot
9 1,637
Hello all, I have a question: assume in matrix M(n*n), each element M(i,j) of matrix is computed as M(i&)*M(&j) /...
Jan6-13 01:06 PM
sanaz
4 1,002
I have some technical questions about spans and bases which my textbook really does not cover very well. I would...
Jan6-13 06:16 PM
AlephZero
2 925
I am a bit confused about the page that I attached... I don't understand part (ii)... How can you compute XX? So...
Jan6-13 12:07 AM
Artusartos
6 838
I have no idea what this is! Please can someone explain comparing to a 3x3 matrix?
Jan6-13 05:19 PM
mfb
3 1,107
No not the trival solution but generally GCD(x,y) = 1 when GCD(A,B)=1 x =...
Jan7-13 12:40 AM
ramsey2879
0 1,012

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