This word has much more versatility than any of the following English
partial-equivalents: "eigenvector", "eigenspace", "generalized
eigenspace", "eigenvalue". It captures their underlying relationship,
similar to what the prefix "eigen-" alone manages. We also gain the
ability to speak of the linear transformation at hand (as sort of
'eigentransformation', if you will); while linear transformation x2 is the
least restricted of the terbri (since all linear transformations have
eigenvectors and eigenvalues by this definition, namely the zero vector
and the scalar zero (0) respectively), the shading of thinking not of any
old linear transformation but one which we are interested in its
eigenthings eludes English. We also win because we can easily generalize
eigenspaces and specify by what exponent (x4) we are doing so; English
does not even have a term for this exponent- I was forced to call it the
"eigenspace-generalization exponent"!

This term also includes the natural eigenvector of the zero vector and the
natural eigenvalue of the scalar zero (0). In most English mathematics
culture to which I have been exposed, these objects are explicitly
excluded from these groups, which is less pretty and natural.

Comment #3: Re: Fun Insight

Curtis W Franks (Fri Jan 3 11:08:01 2014)

krtisfranks wrote: > excluded from these groups, which is less pretty and natural. I do not mean "group" in the mathematical sense, although...