Finding a Transformation Matrix to yield the basisby silvermane Tags: basis, matrices, solution space, transformation 

#1
Oct510, 11:08 PM

PF Gold
P: 117

1. The problem statement, all variables and given/known data
The solutions to the linear differential equation d^2u/dt^2 = u for a vector space. Find two independent solutions, to give a basis for that solution space. 3. The attempt at a solution I want to understand this question. I feel that there's something I'm missing. I believe that I need to find the Transformation Matrix, but I need to understand how :( Any hints or tips are greatly appreciated, but please don't give me just an answer! :))) 



#2
Oct510, 11:18 PM

P: 351

I don't really think you're looking for a transformation matrix here. You have some vector space, with a vector u. There are a bunch of vectors (an infinite number, in fact!) in the space that solve the equation [itex] u'' = u [/itex]. What you want is a way to write down any vector that solves that equation as the sum of two other vectors (that you are going to find).
Now, what vectors solve this equation? 


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