Architecture - A definition you can get your hands around?

Architecture seems to be used all over the place, and unless you are building a house, the word seems to differ with each use.  I've struggled with the less well defined terms and concepts in Enterprise Architecture such as: architecture, viewpoint and view.  Sometimes everything makes sense.  Other times, not so much.  Here are some thoughts that might make it all easier to grasp.

For large enterprises, architecture has evolved to describe the enterprise and the logical decomposition of its elements. The purpose in the evolution of architecture is to enable visibility of appropriate levels of detail from relevant perspectives.

For those who are mathematically inclined, I introduce the following description:

First, think of an enterprise information set which includes all the data and the information of that enterprise and capture all that information in a multidimensional matrix we will call E.

Second, define a multidimensional matrix, IX, which is has dimensions less than E, and the subscript X can have values X=O, Sys, Ser, T or other. IO will correspond to the identity matrix for an Operational viewpoint; ISys will correspond to the identity matrix for a Systems viewpoint; ISer will correspond to the identity matrix for a Services viewpoint; IT will correspond to the identity matrix for a Technical Standards viewpoint; and, Iother matrices will correspond to the identity matrix for any other viewpoints.

Taking the product of the matrix E and the matrix IX is defined as EX. EX is the view based on the X viewpoint. In equation form

E * IX = EX

There is no definition of these matrices beyond this conceptual level.

In words, if I look at the enterprise from a particular viewpoint such as systems, then what I see is the systems view of the enterprise. In Enterprise Architecture common viewpoints are systems (also known as products), services, functional and operational. Other, less common, viewpoints are financial and communications. Any perspective however, can generate a view of the enterprise. A perspective has value when it provides insight into the enterprise for decision makers.

If we want to define the architecture for the global (actually, transnational) space enterprise, we must include the common views at a minimum.