eigenstuff
Hello...
So, I know what an eigenvector is, and its corresponding eigenvalue. So let's just refresh with the definition:
Ax = (lambda)x
Where A is a matrix, x is a column vector, and lambda is a scalar value. "x" is the eigenvector of A since the multiplication of A times x gives the same result as the multiplication of the scalar lambda times x. Lambda is the eigenvalue corresponding to eigenvector x.
So....why is this important? I know what an eigenvector is, and I think at some point I had to find them by hand, but now I see them everywhere in what I am reading and I'm not sure why they're so interesting to people. Can I visualize them with some straightforward geometric interpretation? I'm hoping that some benefactor of mathematical knowledge will read this and give me an insightful answer. Right?