Recent content by evalover1987

actually, i used a slightly different method to solve it, treating it as finding a null-space to solution of a determinant function at the point (0, 0, 1, 1). Do you mind taking a look at the new problem I posted? I'm really struggling with that..

Homework Statement Let's assume that M is a compact n-dimensional manifold, then from Whitney's Immersion Theorem, we know that there's an immersion, f: M -> R_2n, and let's define f*: TM --> R_2n such that f* sends (p, v) to df_x (v). Since f is an immersion, it's clear that f* must be...

actually, I thnk I got it. thanks for the help, thou :)

yeah... while I believe that 0 1 0 0 0 0 1 0 two traceless matrices should be basis elements of tangent space, since 2 by 2 matrices having rank 1 can be thought of as 3-dimensional submanifold, the tangent space must also have 3 basis elements. so I was wondering maybe...

thanks for help, and I again apologize for my rudeness in the previous post

actually, in addition to traceless matrices, shouldn't the original matrix 0 0 1 1 be included in the basis for tangent space?

sorry I misunderstood you. unfortunately, i cannot open ps file. (unless it's converted to pdf) i guess i'll look for some other references.

tracelessness is clearly not required for det(A) = 0. 1 0 0 0 1 1 1 1 are not traceless. I'm just trying to figure out what formula to use to find out the tangent space at the matrix A. Does it mean that if B is in tangent space at matrix A, then BA = 0 ? or...

Homework Statement Homework Equations The Attempt at a Solution

you know what? i solved it. you don't have to continue to reply to this. plus, it's not a "hint" if it's something that I already proved on my own.

true. but with all due respect, you're not adding anything to what I've done so far. my problem was that I am not quite sure how to prove the existence of z, x such that they are not equal to each other, and g(z) > 0 and g(x) < 0 (or g(z) <= 0 and g(x) > 0) so that I can apply...

yeah, i did that, but i failed to show that g(z) must be zero for some value of z, and that was exactly the problem I had. If I can show that if g(z) > 0 for some value of z, then g(x) < 0, for some value of x that's not equal to z, then I can apply an intermediate value theorem to solve it...

Homework Statement Let S denote a unit circle centered at origin in xy plane, and f is a continuous function that sends S to R (no need to be 1 to 1 or onto). show that there's (x, y) such that f(x, y) = f(-x, -y) Homework Equations have a feeling it has something to do with theorems...

my bad, problem fixed. i meant b_n < = b_1

Homework Statement let's define {b_n} as an infinite sequence such that all terms are nonnegative, and for any i, j >= 1, b_{i+j} <= b_i + b_j it's easy to show that b_n/n <= (b_1) for all n, but how would you show that {(b_n)/n} is a convergent sequence?Homework Equations The Attempt at a...