# norm

1. ### How can I find the resultant and norm from pair of vectors passing in half a circle?

I've been walking in circles (no pun intended) with this problem. It states as follows: A certain sugar is analyzed at an optical laboratory. The tecnician passes two beams in the visible spectra one orange and the other lightblue. These describe the vectors labeled A and B (see the figure...

4. ### How to find the rotation matrix to minimize L1 norm

Hi, assuming we have two Nx3 matrices, A and B I want to find a 3x3 rotation matrix R in SO(3), st. min |AR-B| where |*| is the L1 norm. anyone know how to do it? thanks. I know how to do it when using L2 norm..
5. ### Vectors and Norm

Hello, Im learning Calculus in CS so I have couple questions on vectors. 1. vector -v = [v1,v2] ; and need to proof - 1/ ||v|| * v =1 so 1/||v|| is a scalar according the formula - ||v*t|| = |t|* ||v|| || (1/ ||v||) * v || = | (1/ ||v||) | * || v|| (1/ ||v||) * || v||...
6. ### Proof concerning matrix norm.

Hi, I am struggling with following proof, could you give me some hint or some information which would help me in proving following inequality?
7. ### Proof concerning eigenvalue and matrix norm.

Hi, I am struggling with the following proof. I think I know how to prove the right hand side inequality |lambda| <= ||A||, but I still don't know how to prove the left hand side inequality. Could you please give me some hint ? :)
8. ### Vectorial norm help

Hello, I am new to the forums. I was not sure if this question should be asked in this section, but as the exercise is from my calculus course I have posted it here. Here is the question: Does the function ||(x,y)||=max{|x+y|,|x-y|} define a function in R2? I am having trouble in proving (or...
9. ### Gradient of squared norm

I have to find gradient of norm(x'Ax'-b) where x is a vector and A is a 4x4 symmetric matrix. I am trying to solve it by using identities given in https://en.wikipedia.org/wiki/Matrix_calculus but I am not able to figure out which identity suits my problem. I would appreciate if anyone tells me...
10. ### how do I prove the existence of this norm?

I am reading an article[1] that states: Let $\mathbb{K}$ be a fixed local field. Then there is an integer $q=p^r$, where p is a fixed prime element of $\mathbb{K}$ and r is a positive integer, and a norm $\left | . \right |$ on $\mathbb{K}$ such that for all $x\in \mathbb{K}$ we have \$\left |...
11. ### Excercise with inner product

Hello, thank you for accepting me. I am studying mathematics, and I have a problem with an excercise which I don't even know if I have placed it in the correct board. Excercise We know that we can define the norm of a function f via the inner product as follows: ||f||=(fâ€¢f)^(1/2) If we...
12. ### Derivative of norm of a Gram matrix's diagonal

I have a matrix X of size m-by-n. I need to calculate derivative of the following function of X with respect to X: f(X)=||diag(X^TX)||_2^2 where diag() returns diagonal elements of a matrix into a vector. How can I calculate \frac {\partial f(X)} {\partial X}? Please help me. Thanks in...
13. ### Energy norm from Variational formulation (FEM)

If I've stated a differential equation in a variational (weak) form, is there a general algorithm to yield an expression for the energy norm of the solution? For instance, the problem: \begin{split} -\nabla (a(x,y)\nabla u) &= f,\;\;\;x\,\epsilon\,\Omega \\ u &=...
14. ### norm of proj vs, proj

hi I am confused, what is the difference between the norm of a projection and a projection ... particularly when apply projections to problems of the distance between a point and a plane. Isn't it enough to find the projection of the vector normal to the plane, on the vector, ( x0-x1...
15. ### Holder Space Norm

The Holder Space C^{k,\gamma}(\bar{U}) consists of all functions u \in C^{k}(\bar{U}) for which the norm ||u||_{C^{k,\gamma}(\bar{U})} := \sum_{|\alpha| \leq k}||D^{\alpha}u||_{C(\bar{U})} + \sum_{|\alpha| =k}[D^{\alpha}u]_{C^{0,\gamma}(\bar{U})} is finte. How would you interpret the second...
16. ### inequality with norm

Let x_1, \ldots, x_{2m}be \{0,1\} Bernoulli random variables, i.e. variables which takes values 0 and 1 with equal probability. Let S_mbe group of all permutations \pion\{1, \ldots, m\}with uniform distributions. Denote ||\cdot||_p=(\int_{S_m}|\cdot|^p d\pi)^{1/p}. How to show the following...
17. ### a mixture distribution norm and exp, help!

i use matlab to create a mixture distribution norm and exp. the pdf and cdf are defined: pdf_mixture = @(x,p,mu1,mu2,sigma1)p*normpdf(x,mu1,sigma1) + (1-p)*exppdf(x,mu2); cdf_mixture = @(x,p,mu1,mu2,sigma1)p*normcdf(x,mu1,sigma1) + (1-p)*expcdf(x,mu2); and this is the graph...
18. ### Best approximation in norm of f(x)=x

Hey I am trying to calculate the best approximation of f(x)=x (in norm) using a function of the form a*cos(x) + b*sin(x). The interval is [0, pi]. I am supposed to use fourier theory in order to solve this problem, but I am not sure how. Thanks :)
19. ### product rule in norm space

the product rule fn->f , gn->g implies fngn->fg true in the normed vector space (C[0,1],||.||) depends on the the norm||.||. Give a proof or a counterexample for (C[0,1],||.||infinite),(C[0,1].||.||1) HINTS:For counterexample , you may wish to examine the case f=g=0 and choose fn=gn for some...
20. ### integral norm proving

show that ||f||1 = ?|f| (integral from 0 to 1) does define a norm on the subspace C[0,1] of continuous functions (there are 3 conditions , i just dont know how to prove that ||v||>0,||v||=0 implies v=0) and also the same for ||f||= ?t|f(t)|dt is a norm on C[0,1]