I am a complex systems researcher and I need to have complete knowledge about eigen vectors and eigen values. How does change in dimension affect a point's eigen vector and eigen value? What does principal eigen vector and principal eigen value mean for a point of n-dimension?
Thanks in advance.
By Points, I meant, nodes in a network. It's true a node doesn't have an eigen value unique to itself. But, the entries in the principal eigen vector is unique for each node in the network. So, if I isolate a node, or add a new node, the dimension changes. So, what effect will this have on the principal eigen value and the entries of the principal eigen vector when compared to the previous value?
First of all, what does, principal eigen value and principal eigen vector mean for a node in an n-dimensional network?