Recent content by Enjoicube

Haha, took a walk and that's exactly what came to me. I think I had a proof of a similar theorem stuck in my head and wanted to follow that technique.

Nevermind continuity, I don't think the continuity of f directly matters in this situation. However, maybe a start on the problem would be to assume that f is not uniformly continuous, and then, picking an epsilon e>0, for each n, pick one x in X such that |fn(x)-f(x)|>=e, and so create a...

Homework Statement Alright, here is the problem. Given a compact metric space X, and a sequence of functions fn which are continuous and f_{n}:X->R (reals), also f_n->f (where f is an arbitrary function f:X->R). Also, given any convergent sequence in X x_{n}->x, f_{n}(x_{n})->f(x). The problem...

Hello All, I am trying to understand something I read in an article about magnetars and pulsars. The article states that when a magnetic object, such as a star, is compressed, the magnetic field strength increases. Intuitively, this seems true, as the number of field lines will remain...

Now that the age of drinking is upon me, I have given a bit of thought to this. To be honest, I don't think my drinking habits will change, I have 1 beer every 6 months or so. I am not opposed to drinking, but I don't have any time for it, during the school year I have too much work to even...

Yes, I think this revealed a lot to me. I think that I was just being very cautious, because the notation was very suggestive, and so I went into some sort of lockdown mode. I do like the way of conceptualizing this that you presented, and now I do understand that in the complex case it is...

Thank you for your responses, I think I have proved that for real unitary matrices, the transpose really is just the transpose. here is my proof if anyone can check or is interested. Lemma: If U is unitary real, then it commutes with the matrix rep. of a nondegenerate bilinear form. Pf: Let U...

Even for some random inner product, I think this is what I don't understand, why must it be the normal transpose for any completely random product, it only seems true for R^n with the standard dot product. Like for example, taking the space to be the space to be Pn(X) and <,> to be the integral...

Homework Statement Prove that the determinant of a unitary matrix is +/-1 Homework Equations <Av,Aw>=<v,w> Det(AB)=Det(A)*Det(B) The Attempt at a Solution Alright, I am aware that <Av,Aw>=<v,w> => A(tA)=I and (tA)A=I so Det(A(tA))=Det(I)=1 thus Det(A)*Det(tA)=1. However, this is where I am...

Yes, now I realize that RGB is not the only basis for color space, and of course three dimensional vector space has infinite number of different bases, however, for example, it would be quite thoughtless to choose {34(x^2)+23x+5,87x+54,798} as a basis for the space of polynomials of degree 2...

Very very odd and interesting. Seems that Yellow, Magenta and plain blue can also be a basis, as Cyan=Red+Green Magenta=Green+Blue Blue=Blue Now, if these are expressed in matrix form, as (1,1,0) (0,1,1) (0,0,1) Then they are in echelon form (and expressed in terms of basis...

Maybe you should investigate it through fractional calculus: http://en.wikipedia.org/wiki/Fractional_calculus. See whether the negative derivative is an inverse?

Since prime colors cannot be created by any combination of any other colors, and since composite colors are combinations of the prime colors by definition, does this mean that the prime colors could form a basis for a space of colors? If you split up a color into components, like real vectors...

I suppose the same argument goes for the trig functions sine and cosine, since they are linearly independent.

Here is something that always bugged me, and I think I have an explanation for it now, but I am wondering if it is correct. Alright, the problem to me was that back when I was in Diff-eq, to use undetermined coefficients with polynomials, we would always group together the terms on one side, and...