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 valsi tegei'ai type cmavo-compound creator krtisfranks time entered Fri Jan 3 10:07:58 2014

Examples

English
Definition #44180 

selma'o BAI
definition aigne modal, 3rd place: with (generalized) eigenspace (eigenvector vectorspace) ...
notes Not "in eigenspace ..."; use klesi, le'a, or in particular cmima for that usage. Since ve aigne is by default 1 (unless explicitly or contextually implicitly specified otherwise), tegei'ai will typically/by default refer to a strict/simple eigenspace (wherein the generalization exponent is 1); in order to override this default and explicitly specify that the 'eigenspace' at hand is generalized, mark it as such (perhaps using vegei'ai) parenthetically, by clause, or in subscript. Note that a freestanding vegei'ai will not necessarily restrict the referent of tegei'ai to some/the specified generalization of eigenspace, since a given linear transformation can have many generalized eigenspaces for the same eigenvalue (simply differing only by generalization exponent). Eigenspaces retain the operations and properties endowing the vectorspaces to which they belong (as subspaces). Thus, an eigenspace is more than a set of objects: it is a set of vectors such that that set is endowed with vectorspace operators and properties. Thus klesi alone is insufficient. Eigenspaces are sometimes denoted by "E" with subscript lambda (for the eigenvalue of interest) and superscript "T" or "A" (for the linear transformation or respectively square matrix of interest); these are cultural conventions. Always includes the zero vector. May or may not be degenerate. See also: aigne, gei'ai, segei'ai, klesi, le'a, cmima
gloss words
created by krtisfranks
vote information 0
time Fri Jan 3 10:39:13 2014

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