Then i think my conception of adding vectors is incorrect. If i think of vectors as directed line segments, i cant think of a way to add vectors on the x-axis to other vectors to get something parallel.
But if you add a vector to the x-axis, how can that be a line parallel to the x-axis. More importantly, what is an element of the x-axis? Is it just a point?
I'm having a bit of trouble seeing Vector Quotient Spaces.
Lets say I have a vector space $V$ and I want to quotient out by a linear subspace $N$. Then $V/N$ is the set of all equivalence classes $[N + v]$ where $v \in V$.
For example, let me try to take $\mathbb{R}^{2} /$ x-axis. This...
Hello,
I am currently a high school student and I have been accepted into both UC Berkeley and the University of Chicago. I plan to major in math or physics, but I have no idea which college I want to go to. From what you know of their undergraduate mathematics or physics programs, which...
This site was linked at the top of the physics forums website. www.relativitychallenge.com I guess everybody has freedom of speech. Do people just get a kick out of proving Einstein wrong?
This problem comes from Halmos's Finite Dimensional Vector Spaces. Given that we can re-define addition or multiplication or both, is the set of all nonnegative integers a field? What about the integers? My thinking is that since the Rational numbers form a field, and they are countable, we...
Has anyone read Cours d'analyse mathématique (Course in Mathematical Analysis)? If you have, do you find some the the problems just a might challenging? I've found that this is pretty characteristic of books of that time period. Why have problems in textbooks today gotten so much easier?