Is there a relation between half space and Eigenvectors?

Question

I request earnestly apology if the question is not well defined. I think I understand half space and Eigenvectors to an extent, but could not connect both of them under the same geometry or ''umbrella''. I am sure I am missing something. So is there any way to visualize them together? In other words is Eigenvector related to half space somehow?

Answer 1

I think tensors are a possible connection, more specifically the Transient Green tensor.

For more general themes, you may want to take a look at the following articles. From what you have described, you would probably be really interested in Poincaré and Siegel Half planes and the geometric generalizations:

Here are some articles which hopefully answer your questions:

General Half space definition: http://en.wikipedia.org/wiki/Half-space_(geometry)#Upper_and_lower_half-spaces

Siegel Half space: http://en.wikipedia.org/wiki/Siegel_upper_half-space

Poincaré half plane model: http://en.wikipedia.org/wiki/Poincaré_half-plane_model

And Hilbert modular space forms: http://en.wikipedia.org/wiki/Hilbert_modular_form