These section were trying to find a solution for y' = Ay, where A is a matrix made up of constants. For a system of dimension n there will be a set of n linearly independent solutions. In dealing with these solutions, the idea of an eigenvalue was introduced. w is an eigenvalue of A if there is a nonzero vector v such that Av = wv. v is called an eigenvector. The eigenvalues of A are the roots of its characteristic polynomial p(w) = det(A - wI), where I is the identity matrix. The next section moves into 2-D systems are theorems for the general solutions to the systems are given.
Challenges
Many. From the beginning I was lost as to why we were dealing with the equation y' = Ay, with A being a matrix. Then in the second section with the complicated general solutions I was even more lost.
Reflections
It was interesting material but I think I got a little scared off by the eigenvalues and eigenvectors since I lack linear algebra experience.
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