Recent content by cristina89

Hello people! I'm studying about collineation. It seems to be simple, but I can't understand so much and I can't find so many things about this subject... Can someone explain to me what exactly is a Collineation? Is this the same thing as Affine Transformation? Is there examples that...

Thank you so much! :)

Homework Statement Given the matrix 2 0 0 0 0 0 0 1 2 0 0 0 0 0 0 1 2 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 2 What is the minimal polynomial? Homework Equations - The Attempt at a Solution This is the Jordan form, so I guess the solution is just...

Homework Statement Prove that if f(x)<=g(x) then lim f(x) <= lim g(x).Homework Equations -The Attempt at a Solution I've tried by definition of limit, but I didn't get anywhere with this... Can anyone help me??

I'm trying to solve it by induction. For n = 1 ok. Assuming that's ok for n = k. For n = k+1 I don't know if I'm doing it right in this part: Tk+1 = Tk.T(u+v) = Tk.(T(u+v)) = Tk(T(u)) + Tk(T(v)). Can I just afirm that's ok since T(u+v) is an application and Tk is an application too?

Homework Statement If T is a linear transformation, proof that Tn is a linear transformation (with nEN). Homework Equations I know that T is a linear application if: T(u+v) = T(u) + T(v) T(au) = aT(u) The Attempt at a Solution Actually I don't know how to start using these two...

When the exercise tells me to calculate the flux, how do I know when I need to use each of these theorems (Green's, Stokes or Divergence)? Can anyone tell me the difference between them? I'm a LOT confused about this. If anyone knows any good material about this on internet, it'll help me a...

Homework Statement My teacher solved this in class but I'm not understanding some parts of tis solution. Show that \nabla_i V^i is scalar. Homework Equations \nabla_i V^i = \frac{\partial V^{i}}{\partial q^{i}} + \Gamma^{i}_{ik} V^{k} The Attempt at a Solution To start this...

Homework Statement B is a third order tensor. Show that B^{ij}_{i} is a contravariant vector. The Attempt at a Solution Well... I just thought about a simple solution but I don't think I'm right. But anyways. Considering B^{ij}_{i}. If I raise the index i: g^{ij}B^{ij}_{i} = B^{ijj} And...

Thank you! Is it right to bound the integrals like this \int^{2∏}_{0}\int^{8}_{0}?

Can't I think that \hat{n} = \frac{v}{|v|} = \frac{v_{0}x\hat{z}}{\sqrt{v_{0}^{2}x^{2}}} = \hat{z}? And then \int\int{v_{0}x\hat{z}\hat{z}dS}? Can you explain to me this "\hat{z}\cdot\hat{n} is cos of the slope of the normal (= sin of the slope of the surface)"? :S I can't understand that...

ahh ok. so \int\int{v_{0}x}(\hat{z}\cdot\hat{n})dS = \int\int v_{0}x(\hat{z})\frac{v_{0}x\hat{z}}{\sqrt{v_{0}^{2}x^{2}}} right? What should I do after that? I'm now confused if there is this normal vector in this integral. Is this correct?

Homework Statement The velocity of a fluid is given, in cartesian coordinates (x, y, z), by \vec{v} = v_{0}x\hat{z} being a constant with velocity dimensions. a) Calculate the flux of this vector through the closed surface composed by z-x²-y²=0 and by the plan z=8 limited by the circle with...

Thank you so much! I'll try to find this book tomorrow. I just need to have an idea of how, given a transformation, I find a new basis, a normalized basis, the displacement, gradient, the volume in the new basis... This kind of thing. If anyone else knows any other book, please tell me, it...

I'm studying Vector Calculus right now, and I'll have a test about Coordinate Transformation soon. But the book my teacher recommended (Mathematical Methods for Physicists - Arfken) is way too hard to understand this subject. Does anyone know any good material about this that I can find on...