I'm in the process of doing a quantum physics lab and am having a bit of trouble with uncertainty. The specific things going on in the lab aren't relevant, I don't think, only the general procedure of my calculation. Also, I'm not certain where this question should be asked, so I decided to put...
I've used the following implication (conditional...whatever you want to call it) in a few proofs and was wondering if it's actually is true. I incorporated it into my proofs because it seemed to make obvious sense, but I'm not sure if I'm overlooking something- obvious or subtle.
T \subseteq S...
Homework Statement
Suppose that A is an 8x11 matrix whose kernel is of dimension 5, and B is an 11x9 matrix whose image is of dimension 7. If the subspace kernel(A) + image(B) has dimension 10, what is the rank of AB?
Homework Equations
Rank Nullity Theorem: For an n x m matrix A...
This is a pretty basic limit question regarding the limit,
\lim_{x \rightarrow \infty} (1+\frac{1}{x})^x = e
Wolframalpha gives the following reasoning for this answer:
\lim_{x \rightarrow \infty} (1+\frac{1}{x})^x = e^{\lim_{x \rightarrow \infty} x\ln{(1+\frac{1}{x})}} =...
Homework Statement
The problem was to find the volume enclosed by a sphere of radius "a" centered on the origin by crafting a triple integral and solving for it using cylindrical coordinates.
Homework Equations
x^{2}+y^{2}+z^{2}=a^{2} : Equation for a sphere of radius "a" centered on...
Galilean Electrodynamics?!?
I finished reading The History of Pi by Petr Beckman, thoroughly enjoyed it and wondered what other works/activities the author was involved with. Soo I eventually came across this thing called "Galilean Electrodynamics" (which Beckman apparently had a hand in...