Recent content by seanc12

Couldn't you use the Gram Schmidt Process to orthonormalise those eigenvectors?

So, when is it that P^T A P gives a diagonal matrix? Is it only when the eigenvectors are orthonormal?

Hi guys, thanks for all the feedback. It stills seems to be a little bit of a grey area, so if anyone can clarify all this it would be great!

Ok, I see now. So, why is better to choose othogonal eigen vectors with symmtric matrices (with respect to diagonalisation)?

Ah ok that makes sense. One last thing (I want to get these diagonal matrices down, my lecturer seems to be in love with them), when I get the eigen vectors out, do they need to be orthogonal? Because the ones I used from that question don't seem to be.

Hi micromass. Thank you for the help! I got the answer out :D. Getting rid of that fraction made my life 500 times easier. Thanks again. I have a couple of general questions if anyone could answer them for me would be great. What is the difference between diagonalizing non-symmetric and...

Homework Statement Find a matrix P such that P^{-1}AP is diagonal and evaluate P^{-1}AP. A= [2 5] [2 3] The Attempt at a Solution First off, I Found the Eigenvalues, which turned out to be: \lambda = \frac{5 \pm \sqrt{41}}{2} This gave me the two Eigenvectors...

Hi, thanks for the reply Yeah, sorry about all the typos, I'm new to LaTeX so its a bit hard to follow some of what I'm typing. I actually had my integral with repect to y from x to x^2, it was a typo. I keep getting myself confused with the limits I should take, but hopefully I have it...

Homework Statement Solve the following Double Intergral, and show the answer is the same, regardless of which order you integrate. The integral is between the boundaries y=x and y=x^2 Homework Equations \int\int_R (x^2 + 2y)dxdy The Attempt at a Solution So first of all i integrated with...

Also, howcome the underlines don't show up in my LaTeX?

\int_C \frac{d r}{dt}dt Thanks, So from there can i go ahead and substitute the \frac{d r}{dt} back into the integral? or am i missing a few steps? It seems a little easy. Also, where does the C come into it?

Hi HallsofIvy, thanks for the reply. Yes ofcourse, how could i have been so silly :P wasn't paying attention properly thanks for pointing that out. I understand the RHS, but howcome it is = to dr/dt instead of ds/dt? Also as a note, the C on the integral should be a subscript but it...

Homework Statement Confirm that th definition of th arc length ds^{2}=dr.dr leads to the formula L=\int_{C}\frac{dr}{dt}dt Homework Equations \frac{dr}{dt}=\frac{dx}{dt}+\frac{dy}{dt}+\frac{dz}{dt}dt The Attempt at a Solution I am really unsure of what to do here. I have tried starting at...

So, how do i find K, or the momentum for that matter?

Homework Statement I am trying to get the velocity of an electron which has been accelerated through a potential difference of 1x106 V, so that i can find its momentum.Homework Equations K=(1/2)mv2 v=sqrt(2K/m) The Attempt at a Solution So , K = 1x106eV and m = 0.511x106eV/c2...