Author |
Topic: looking for links to linear alg. (Read 364 times) |
|
Benny
Uberpuzzler
Gender: 
Posts: 1024
|
 |
looking for links to linear alg.
« on: May 5th, 2008, 8:59pm » |
 Quote  Modify
|
I need to learn more about linear algebra and vector and tensor transformations as these
seem important to further study in many advanced topics. Any good resource ideas?
say I had a function such as f(i, j, k) = (x^2)i + (y*z)j + (x)k that I wanted to transform to spherical coordinates.
I went to http://en.wikipedia.org/wiki/Unit_vector#Spherical_coordinates to use the vector transformations as described on wiki. to complete the transformation.
But realized that i did not chose my parameters well enough, and it quickly became a mess. Are there any quick tricks I can use to transform these vectors without using this method of matrices and such?
|
|
 IP Logged |
If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
|
|
|
Benny
Uberpuzzler
Gender:
Posts: 1024
|
|
Re: looking for links to linear alg.
« Reply #1 on: May 6th, 2008, 10:40am » |
Quote Modify
|
Say, i have a function such as
f(i, j, k) = (x^2)i + (y*z)j + (x)k that I wanted to transform to spherical coordinates.
r= Sqrt.(x2+y2+z2)
theta= artan(Sqrt.(x2+y2/z)
phi= arctan(y/x)
inversely,
x= r sin(theta) cos(phi)
y= r sin(theta) sin(phi)
z= r cos(phi)
it's f(x,y,z), but in cartesian coordinates. I basically use the equations for x,y,z , and then transform the unit vectors. f(x,y,z)[cartesian] will give me the vector field at a given point, x,y,z with the vector components in cartesian coordinates. f(rho, theta, phi)[cartesian] gives me the vector field at a given position rho, theta, phi - but the vector quantities are still in cartesian coordinates - I've specified the point in spherical.
|
|
IP Logged |
If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print