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        riddles >> general problem-solving / chatting / whatever >> looking for links to linear alg.
        
(Message started by: BenVitale on May 5^th, 2008, 8:59pm)

Title: looking for links to linear alg.
Post by BenVitale on May 5^th, 2008, 8:59pm

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?

Title: Re: looking for links to linear alg.
Post by BenVitale on May 6^th, 2008, 10:40am

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.