Recent content by sjeddie

I get it. (x,y,z)=(a,0,c) + (0,b,0) where (a,0,c) is in U and (0,b,0) is in Uperp. I didn't know what direct sum is, now I do! Thanks a lot rochfor1, you're awesome :)

Ah I see, thank you rochfor1, the (A^T)(A) = I thing makes a lot of sense :)

Is the definition of an orthogonal matrix: 1. a matrix where all rows are orthonormal AND all columns are orthonormal OR 2. a matrix where all rows are orthonormal OR all columns are orthonormal? On my textbook it said it is AND (case 1), but if that is true, there's a problem: Say...

Let's say we are in R3, and U is the x,z plane, i think then all of Uperpendicular should be some translation of the span of the y axis. Now, since that U and Uperpendicular together form R3, then isn't it true that all vectors in R3 should be contained in either U or Uperpendicular? But given a...

thank you very much rochfor1!

Thanks. So it is possible to have less eigenvectors than eigenvalues (according to wiki's explanation on geometric multiplicity), so is it possible to have no eigenvectors at all for some eigenvalues?

Thank you CompuChip

Is at least one eigenvector guaranteed to exist given that we have found at least one eigenvalue? So, for example, given that we have found an eigenvalue of multiplicity 2 of a matrix, are we guaranteed to find at least 1 eigenvector of that matrix? Why or why not?

Let A, B, and C be nxn matrices, I'm wondering 1. is it possible to simplify (ABC)^5 to expand it ( maybe into something like (A^5)(B^5)(C^5) ) 2. what's the fastest way of solving (ABC)^5? I'm thinking actually multiply ABC out, then diagonalize it. Is there a faster way?

So, you mean that the friction does not act on the bottom contact point of the ball? Or are you saying that because the ball is rolling, it has both pure rotational and pure translational motion, and the translational motion is being slowed by the friction whereas the rotational motion is not...

My prof really confused me. Given a rolling sphere, which way does the friction point to? http://img187.imageshack.us/img187/7968/rolling1.png http://img338.imageshack.us/img338/8753/rolling2.png I think it probably matters if the ball is purely rolling or partially skidding, but I'm not...

But if the string is massless, does that mean the tension will be the same everywhere, and the 2 masses will have the same acceleration?

This isn't a homework question, I just thought of it but don't know how to model the situation Given a pulley system like this http://img101.imageshack.us/img101/2106/pulleys.png suppose the string is massless and the pulleys are massless and frictionless. say m2 is greater than m1, each...

Ohhhh! I get it now, I was considering the man pulling down on the rope as an external force instead of an internal force. Now it all makes sense. Thank you very much Doc Al!

Do you mean something like this? http://img63.imageshack.us/img63/5387/pic1p.png I don't understand how there can be 2 tension forces pulling him up. I mean, 1 is pulling on the box, would the other be pulling on his hand? but isn't his hand pulling down the rope and therefore contributing to...