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degenerate form : ウィキペディア英語版
Degenerate bilinear form

In mathematics, specifically linear algebra, a degenerate bilinear form on a vector space ''V'' is a bilinear form such that the map from ''V'' to ''V'' (the dual space of ''V'') given by is not an isomorphism. An equivalent definition when ''V'' is finite-dimensional is that it has a non-trivial kernel: there exist some non-zero ''x'' in ''V'' such that
:f(x,y)=0\, for all y \in V.
==Non-degenerate forms==
A nondegenerate or nonsingular form is one that is not degenerate, meaning that v \mapsto (x \mapsto f(x,v)) is an isomorphism, or equivalently in finite dimensions, if and only if
:f(x,y)=0\, for all y \in V implies that ''x'' = 0.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Degenerate bilinear form」の詳細全文を読む



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