Recent content by s_j_sawyer

Nevermind I got it. I was overthinking it apparently...

Well \sigma is the steering angle... my professor told us just to assume the boat had a constant speed, which is why I introduced the formula V_x^2 + V_y^2 = 1^2 and in thus doing so assumed the speed to simply be 1. Can someone read the question and see if I'm interpreting...

Homework Statement See attached. Homework Equations The Attempt at a Solution I originally began by assuming the rate was constant, obtaining the equations V_x^2 + V_y^2 = 1 \tan{\sigma} = \frac{V_y}{V_x} with the assumptions V_x(\sigma) = f(\sigma) V_y(\sigma) =...

Homework Statement Determine whether the following in R^2 are compact or not. (i) [0,1] X [0,1) (ii) [a,b] X [c,d] where a < b, c < d The Attempt at a Solution I have seen this notation before but I never knew what it meant.

Ok I followed everything you said but I still don't see how this relates to what I'm trying to show. The fact that there is a /n necessary is really confusing me. i.e. |an| <= K/n and not just KEdit: Ok I may have gotten it. I think the solution is |an| <= |a1|/n and |bn| <= |b1|/n There's...

Homework Statement Let f be a C1 function on [-pi,pi]. Prove the Fourier coefficients of f satisfy |an| <= K/n and |bn| <= L/n n=1,2,... Homework Equations an = 1/pi * int[-pi..pi] (f(x)*cos(nx)) dx bn = 1/pi * int[-pi..pi] (f(x)*sin(nx)) dx Sorry if my form is slightly...

Homework Statement Solve this system of linear ODEs: 1) x''(t) = x + y 2) y''(t) = x + y Just fyi, this is part of a much larger problem but I need to solve this system! Homework Equations See above. The Attempt at a Solution Okay so I think the most logical way to solve...

Sorry to double post but I didn't think simply editing would bump this up. Alright so I played around with this some more but still could not get it to work. I tried to prove this using the method of squaring both sides for the regular 'scalar triangle inequality' proof like so: ||w +...

Oooohhh deeaarr how embarrassing. Thank you for that insightful information. I should be able to get it now.

Homework Statement Let z, w be complex vectors of C^n. Prove ||w + z|| <= ||w|| + ||z|| (using the standard inner product for C^n) (i.e. <w,z> = w*z', where * is the dot product and ' denotes the complex conjugate) The Attempt at a Solution Well, I found that ||w + z|| =...

Well, A has an orthonormal set of n eigenvectors, which would therefore be the same as A^T, but I don't know how to use this in the proof.

Homework Statement Prove that if A is an nxn positive definite symmetric matrix, then an orthogonal diagonalization A = PDP' is a singular value decomposition. (where P' = transpose(P))2. The attempt at a solution. I really don't know how to start this problem off. I know that the singular...

I was just wondering if it was possible to find the singular value decomposition of an nxn matrix such as 1 1 -1 1 I tried this but then when finding the eigenvectors of A^T*A I found there were none (non-trivial anyhow). So, is this not possible? EDIT: How embarrassing I made an...

Homework Statement Okay so the objective here is to express y(t) = cos(t - b) - cos(t) in the form y(t) = Asin(t - c) where A and c are in terms of b.Homework Equations For easy reference, here is a table of identities: http://www.sosmath.com/trig/Trig5/trig5/trig5.html The Attempt at a...

So you're saying x*Ay = x*By does not imply A = B? Also, I've proven that any square matrix can be written as a sum of a symmetric matrix and a skew symmetric matrix (i.e. A = B + C, where A is nxn and B is symmetric, C is skew symmetric) but I can't seem to prove C = 0 using my original...