Homework Statement
What is the Schwartzchild metric. Calculus the 4-velocity of a stationary observer in this spacetime (u). Show that u2 = c2.
Homework Equations
Schwartzchild Metric
d{s^2} = {c^2}\left( {1 - \frac{{2\mu }}{r}} \right)d{t^2} - {\left( {1 - \frac{{2\mu }}{r}} \right)^{ -...
Gilbert Strang, in his book "Differential Equations and Linear Algebra" has a pretty simple proof that every basis of a particular vector space has the same number of vectors. A basis for a vector space is a sequence of vectors that are linearly independent and span the space.
If {w1,...,wn}...
Basically the only way that a system of equations all equal to zero will only have the trivial solution is if its rank (the number of pivot columns) is equal to the number of columns of the matrix. In that case, in reduced row echelon form, you would have 1's in the pivot positions... there...
Thanks. Yeah I pretty much just blew past that without giving an explanation because it was something I learned in linear algebra, and the reason it is true seems pretty obvious to me at this point.
Here is not a real 'proof', but I think an explanation that should make the truth of that...
(sorry for the horrible butchered thread title... should say "determination", not "determining")
1. Homework Statement
In "Principles of Quantum Mechanics", by R. Shankar, a vector space is defined as having dimension n if it can accommodate a maximum of n linearly independent vectors (here is...
Homework Statement
This isn't really a problem. I am just re-reading some section "Classical Mechanics" by John Taylor. I think this belongs in the math section, since my question is mainly about the del operator.
There is just one fragment of one sentence that I want to make sure I am...
(Not an assigned problem...)
1. Homework Statement
pg 244 of "Mathematical Methods for Physics and Engineering" by Riley and Hobson says that given the following two properties of the inner product
It follows that:
2. Attempt at a solution.
I think that both of these solutions are...
Thanks BvU and robphy for your opinions and the links you both postsed. I agree that it is a typo. It is kind of funny that this is actually the first problem in the book and there is a typo. I hope that the rest of the book isn't plagued by errors... fortunately if that turns out to be the...
Homework Statement
Given: Ideal gas equations:
Find S(T,V) for an ideal gas
Homework Equations
Ideal gas equations:
\begin{array}{l}
{\rm{}}\\
U = \frac{3}{2}N{k_B}{\left( {\frac{N}{V}} \right)^{2/3}}\exp \left[ {\frac{S}{{\left( {3/2} \right)N{k_B}}} - {s_0}} \right]{\rm{ }}\\
T = {\left(...