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What is Non-degenerate mean?
In mathematics, specifically linear algebra, a degenerate bilinear form f(x, y) on a vector space V is a bilinear form such that the map from V to V∗ (the dual space of V) given by v ↦ (x ↦ f(x, v)) 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 {\displaystyle f(x,y)=0\,} for all y ∈ V . {\displaystyle y\in V.} referencePosted on 06 Dec 2024, this text provides information on Miscellaneous in Maths related to Maths. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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