# Recent content by SNOOTCHIEBOOCHEE

1. ### Differential Geometry: Coordinate Patches

Sorry i wasnt able to get help in the hw department. figured id try here. Homework Statement For a coordinate patch x: U--->\Re^{3}show thatu^{1}is arc length on the u^{1} curves iff g_{11} \equiv 1 The Attempt at a Solution So i know arc legth of a curve \alpha (t) = \frac{ds}{dt} =...
2. ### Geodesics and straight lines on a surface

Homework Statement Let \gamma be a stright line in a surface M. Prove \gamma is a geodeisc The Attempt at a Solution In a plane we know a straight line is the shortest distance between two point. I am not sure if this applies to straight lines on a surface. Further more, there...
3. ### Group Theory, cyclic group proof

Every cyclic group has a generator. What is your generator in this case? edit: nm already beaten too it
4. ### Differential geometry: coordinate patches

one last bump, can anybody help me on this?
5. ### Differential geometry: coordinate patches

bump, i still need help on this
6. ### Differential geometry: coordinate patches

Homework Statement For a coordinate patch x: U--->\Re^{3}show thatu^{1}is arc length on the u^{1} curves iff g_{11} \equiv 1 The Attempt at a Solution So i know arc legth of a curve \alpha (t) = \frac{ds}{dt} = \sum g_{ij} \frac {d\alpha^{i}}{dt} \frac {d\alpha^{j}}{dt} (well thats actually...
7. ### Inner product with (1,1) tensors: Diff. Geometry/ Lin algebra

Ok but as written, how do you compute that complex inner product?
8. ### Inner product with (1,1) tensors: Diff. Geometry/ Lin algebra

Homework Statement Given g\equiv g_{ij} = [-1 0; 0 1] Show that A= A^{i}_{j} = [1 2 -2 1] is symmetric wrt innter product g, has complex eigenvalues, but eigenvectros have zero length wrt the complex inner product. The Attempt at a Solution Im sure this is just a simple...
9. ### Questions from a probabilty final

Homework Statement Few questions here, nothing super tough, just cant get it/ want verification. 1. The following experiment is repeated twice: a fair coin is flipped repeatedly until it lands heads. Let X be the number of flips required in the first trial and Y the number required in...
10. ### Probability: unfair coin toss, probably pretty easy

Thanks dick, sorry you wasted your 12k post on me :/
11. ### Probability: unfair coin toss, probably pretty easy

Ok i calculated this out and got 20/26 which is the correct answer, but can you explain how you came to this formula?
12. ### Probability: unfair coin toss, probably pretty easy

Homework Statement A biased coin lands heads with probabilty 2/3. The coin is tossed 3 times a) Given that there was at least one head in the three tosses, what is the probability that there were at least two heads? b) use your answer in a) to find the probability that there was...
13. ### Linear algebra/ optimization proof

Homework Statement A vector d is a direction of negative curvature for the function f at the point x if dT \nabla ^2f(x)d <0. Prove that such a direction exists if at least one of the eigenvalues of \nabla ^2 f(x) is negative The Attempt at a Solution Im having trouble with this...
14. ### Find the decomposition of the standard two-dimensional rotation

Homework Statement Find the decomposition of the standard two-dimensional rotation representation of the cyclic group Cn by rotations into irreducible representations The Attempt at a Solution Ok i did this directly, finding complementary 1-dimensional G-invariant subspaces. but...
15. ### Proving Convexity

we can show a set is convex for for any elements x and y ax + (1-a)y are in S. for a between 0 and 1. but i dont know how to use that here.