This problem comes right out of my linear algebra test review. I thought it was such a great problem I would share it with our reader(s?)
Let E be a basis for a finite dimensional vector space V and F a basis for another finite dimensional vector space W. Let A be the matrix representing a linear transformation L : V -> W relative to E and F. If G is another basis for V, and S is the transition matrix from G to E, and B is the matrix representing L relative to G and F, what is the relationship between A and B? If H is another basis for W, and T is the transition matrix from H to F, and C is the matrix representing L relative to G and H, what is the relationship between A and C?
Don't worry, I am just as confused as the next guy when I read it, but the TA did give me this hint: he said that the answer was somehow related to the number of beta phase carbon atoms in a square pico meter of a lime gummy bear.
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3 comments:
Well thank goodness for that clear-as-glass hint! I'd never figure it out otherwise. :)
WWWWHHHHAAATTTT?????
Ahhh, Kevin. This is Tess's greenie. Don't worry, when I read that the only thing I thought of was 'oh help, someone get me some scratch paper.'
I had to take that class too and I still have no idea how to solve any of those problems, but I DO have a civil engineering diploma sitting on my office wall right now.
My biggest problem in that class was that I kept wondering who built a building, road or waste water treatment plant in vector space V as defined by finite dimensional vector E?
Good Luck out there!
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