
Please post any and all homework or other textbookstyle problems in one of the Homework & Coursework Questions...

Feb2313 09:24 AM
micromass

1 
35,153 

 
 
 
While studying YangMills theory, I've come across the statement that
there exists a positivedefinite inner product...

Y 11:23 AM
Terandol

1 
123 
There are two "formal" definitions of vectors (and tensors in general) which I've learned.
The first is what I...

Jul3014 06:09 PM
micromass

15 
230 
Hi PF!
Can you please tell me why it is beneficial to use SVD in data processing? My understanding is, given a lot...

Jul3014 01:54 PM
Stephen Tashi

10 
270 
Hi, 2forms are defined as
du^{j} \wedge du^{k}(v,w) = v^{j}w^{k}v^{k}w^{j} = \begin{vmatrix} du^{j}(v) &...

Jul3014 09:34 AM
JonnyMaddox

0 
85 
Hello. I need some help. I am not a math wizard by any means, but I find myself in need of math right now. I have...

Jul3014 07:58 AM
Erland

15 
508 
The killing form can be defined as the twoform ##K(X,Y) = \text{Tr} ad(X) \circ ad(Y)## and it has matrix components...

Jul2914 01:19 PM
center o bass

0 
84 
In my limited study of abstract Lie groups, I have come across the adjoint representation ##Ad: G \to...

Jul2914 01:46 AM
WWGD

1 
335 
(I don't like the title, since it is a bit misleading. But, I couldn't think of a more descriptive title that fit in...

Jul2814 01:01 PM
Nick O

0 
95 
Hello,
I am trying to understand the slides in the PDF I posted. I am looking particularly at slides 2024. I am so...

Jul2714 05:57 PM
AlephZero

13 
572 
Hi, all. I'm in desperate need of assistance with a matrix I can't get my head around of. I want to solve a system of...

Jul2614 04:32 PM
skujesco2014

1 
360 
This should be really easy, but I can't seem to find the answer. What does the symbol ##\ominus## mean in the context...

Jul2614 06:45 AM
HallsofIvy

2 
359 
Hi,
I have a rather trivial question but google did not really help me. So far I was always familiar with the fact...

Jul2414 11:23 PM
divB

5 
596 
I heard about fast tridiagonal matrix algorithm. I tried to find what is it but I can only find tridiagonal matrix...

Jul2314 11:58 AM
Shyan

0 
466 
Just one simple doubt here.
Can we use different scales on the x and y axes be used for denoting linear...

Jul2214 06:48 AM
HallsofIvy

2 
832 
I know it should be absolute zero, but in a scientific calculator, which is an app actually, its value is shown...

Jul2114 05:34 AM
Adit

3 
500 
Hello,
I am going over these slides and I am very confused on a couple parts. First of all on the first slide, I...

Jul2014 01:19 PM
WWGD

6 
590 
Hello everyone!
I've been learning some basic group theory (I'm new to the subject). And I had a (hopefully) fairly...

Jul1914 06:37 PM
WWGD

3 
576 
Hi,let:
0>A> B > 0
; A,B Zmodules, be a short exact sequence. It follows A is isomorphic with B.
. We...

Jul1914 03:16 PM
WWGD

4 
1,461 
Problem 1: Use Gaussian elimination with back substitution to solve the following system.
Problem 2: Use the...

Jul1914 12:38 PM
micromass

6 
957 
Hi,
Given several vectors, which may be or not be orthogonal to each other, how to construct a vector perpendicular...

Jul1814 06:25 PM
WWGD

4 
747 
I am working with polytopes that are defined by halfplanes in \Re^N. So they are defined by a number of inequalities...

Jul1814 04:11 PM
sloppyintuit

2 
710 
Hi All,
Let A,B be algebraic structures and let h A>B be a bijective homomorphism.
Is h an isomorphism? In...

Jul1814 12:01 PM
WWGD

2 
897 
Use Gaussian elimination with back substitution to solve the following system:
x1+x2+x3=1,
x1+2x2+2x3=1,...

Jul1714 09:34 PM
Math10

3 
1,066 
Hello,
Been a long time lurker, but first time poster. I hope I can be very thorough and descriptive. So, I have...

Jul1614 04:02 AM
nikphd

4 
1,454 
Hi all,
Suppose I have a matrix A_{N\times N}. I compute its eigenmodes
A V = V \Lambda.
V, \Lambda are...

Jul1514 08:06 PM
AlephZero

1 
1,182 
The killing form on a lie algebra is defined as
$$B(X,Y) = \text{Tr}ad_X \circ ad_Y$$
where ##ad_X: \mathfrak{g} \to...

Jul1414 05:44 PM
Terandol

1 
1,481 
Hello,
Given the complex linear mapping: T(z) = Az + B where A is real and B is complex. However trying to show...

Jul1414 03:57 PM
WWGD

3 
1,197 
The definition (taken from Robert Gilmore's: Lie groups, Lie algebras, and some of their applications):
We have...

Jul1414 01:22 PM
Travis091

6 
1,370 
Two groups are isomorphic if they has same number of elements and if they has same number of elements of same order?...

Jul514 05:24 PM
NeoAkaTheOne

12 
5,677 
Can you guys give me a concrete example of a completely positive map from M_m → M_n?

Jul314 06:26 PM
WWGD

2 
2,456 
Hi,
i was wondering how the following expression can be decomposed:
Let A=B°C, where B, C are rectangular random...

Jul214 04:54 PM
MisterX

2 
2,524 
I am trying to diagonalize the following matrix:
M =
\left( \begin{array}{cccc}
0 & 0 & 0 & a \\
0 & 0 & a &...

Jul214 12:45 PM
Trifis

2 
1,983 
I need help solving for t in the following equation,
P + Vt + A(t^2)/2 = st
where P V and A are vectors and s...

Jun3014 04:45 PM
jedishrfu

3 
2,250 
I've been reading about algebraic geometry lately. I see that a lot of authors use ##V^\vee## to denote the dual space...

Jun2914 10:45 AM
Mandelbroth

2 
2,693 
Hi.
In this development
(c ∇+ d A)(c ∇+dA)= c^{2} ∇^{2} + d^{2}A^{2} + cd A∇ + cd ∇A
(c ∇+ d A)^{2}= c^{2} ∇^{2}...

Jun2814 11:49 AM
Fredrik

9 
2,126 
Hi, Can someone explain me the division operation in the picture. First for left division we use (.\ ) not only ( \ )...

Jun2614 06:22 PM
HallsofIvy

4 
2,084 
I was reading in my textbook that the scalar product of two complex vectors is also complex (I assuming this is true...

Jun2314 08:16 AM
Fredrik

4 
1,984 
Hello,
first of all, sorry if my question is either trivial or imprecise, I'm from the engineering domain :)
I...

Jun2314 06:26 AM
Erland

1 
1,951 
Hey,
So I am trying to do a triquadratic curve fit (linear regression) in excel. I have successfully completed a...

Jun2014 11:37 AM
mattskie

2 
2,017 