Euclidean space Definition and 58 Threads

Homework Statement Find the maximum of \frac{x+2y+3z}{\sqrt{x^2+y^2+z^2}} as (x,y,z) varies among nonzero points in R^{3} Homework Equations I'm not sure. The section in which this problem lies in talks about scalar products, norms, distances of vectors, and orthognality. However, I...

Homework Statement V is a three-dimensional euclidean space and v1,v2,v3 is a orthonormal base of that space. Calculate the Matrix of the reflection over the subspace spanned by v1+v2 and v1+2*v2+3*v3 . Homework Equations The Attempt at a Solution To determine the matrix I...

I am having some troubles understanding the following, any help to me will be greatly appreciated. 1) Let S1 = {x E R^n | f(x)>0 or =0} Let S2 = {x E R^n | f(x)=0} Both sets S1 and S2 are "closed" >>>>>I understand why S1 is closed, but I don't get why S2 is closed, can anyone...

When dealing with real valued functions (one output for now) of more than one real variable, can the usual rules from R --> R be generalised in the natural way? Specifically the sum, product, quotient and composite rules. Any pathological cases? Also I was also wondering if there are any...

I have read that the Killing vectors in a 3D euclidean space are the 3 components of the ordinary divergence plus the 3 components of the ordinary rotational. I have being trying to find a derivation of this but it isn´t being easy. I really apreciates any clues. Thanks

Hi Can someone explain the difference between Euclidean and Non Euclidean Space and how does one classify a space as Euclidean or Non Euclidean?? I heard about Gauss coming up with Non Euclidean Spaces when he was doing surveying of a piece of land. I am wondering what the word 'FLAT' really...

hi, for most of you this might be a simple question: Is it possible to embed the flat torus in Euclidean space? If we, for example, take a rectangle and identify the left and the right sides we get a cylinder shell, that can be embedded easily in R^3. If we construct the...

A triangle in Euclidean space can be described as having a hypotenuse of one, and legs of Lorentz parameters \beta and \gamma. What spatial curvature underlies a triangle with hypotenuse one, and legs 1/ \beta and 1/ \gamma?