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nullity (Definition)

The nullity of a linear mapping is the dimension of the mapping's kernel. For a linear mapping $T:V\rightarrow W$ the nullity of $T$ gives the number of linearly independent solutions to the equation $$T(v)=0,\quad v\in V.$$ The nullity is zero if and only if the linear mapping in question is injective.



"nullity" is owned by rmilson. [ full author list (2) ]
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See Also: rank of a linear mapping, rank-nullity theorem
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Cross-references: injective, equation, solutions, linearly independent, number, kernel, mapping's, dimension, linear mapping
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This is version 3 of nullity, born on 2002-02-19, modified 2006-09-23.
Object id is 2237, canonical name is Nullity.
Accessed 4917 times total.

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AMS MSC: 15A03 (Linear and multilinear algebra; matrix theory :: Vector spaces, linear dependence, rank)
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